Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle materials.This method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in advance.In this paper,a phase field method based on Miehe's approach[Miehe et al.,Comp.Meth.App.Mech.Eng.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic materials.The numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature.Several numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement curve.Furthermore,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed.It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

Effects of second phases on mechanical properties and martensitic transformations of ECAPed TiNi and Ti-Mo based shape memory alloys

TiNi and Ti-based shape memory alloys were processed by equal channel angular pressing （ECAP） at 673-773 K along Bc route to obtain ultrafine grains for increasing the strength of parent phase and improving the functional properties. The effects of both thermodynamically stable and metastable second phases on the mechanical properties and martensitic transformations of these alloys were investigated. It is found that thermodynamically stable Ti2Ni phase has no effect on martensitic transformation and superelasticity of Ti-rich TiNi alloy, thermodynamically stable α phase is harmful for ductility of Ti-Mo-Nb-V-Al alloy, but metastable Ti3Ni4 phase is effective for R phase transformation, martensitic transformation and superelasticity of Ni-rich TiNi alloy. The mechanisms of the second phases on the martensitic transformations and mechanical properties were discussed.

Evolution of second phases and mechanical properties of 7075 Al alloy processed by solution heat treatment

The effects of solution treatment on the evolution of the second phases and mechanical properties of7075Al alloy werestudied with scanning electron microscopy(SEM),energy dispersive X-ray spectrometry(EDS),differential scanning calorimetry(DSC),hardness and tensile tests.The results show that Mg(Zn,Cu,Al)2phases gradually dissolve into the matrix,yet the size andmorphology of Al7Cu2Fe phase exhibit no change with the increase of the solution treatment temperature and time due to its highmelting point.When the solution treatment temperature and time continue to increase,the formation of coarse black Mg2Si particlesoccurs.Compared to the as-cast alloy,the microhardness,tensile strength,and elongation of the sample under solution heat treatmentat460°C for5h are increased by55.1%,40.9%and109.1%,respectively.This is because the eutectic Mg(Zn,Cu,Al)2phases almostcompletely dissolve and basically no coarse black Mg2Si particles are formed.

Effect of ECAP processing on distribution of second phase particles,hardness and electrical conductivity of Cu-0.81Cr-0.07Zr alloy

The effect of equal-channel angular pressing(ECAP)processing at room temperature and 300℃on the distribution of the second phase particles and its influence on hardness and electrical conductivity of the commercial Cu-0.81Cr-0.07Zr alloy were investigated.Microstructural characterization indicated that the area fraction of coarse Cr-rich particles decreased after ECAP processing.This reduction was attributed to the Cr dissolution induced by plastic deformation.The electrical conductivity of the alloy decreased by 12%after 4 ECAP passes at room temperature due to the increase of electrons scattering caused by higher Cr content in solid solution and higher density of defects in the matrix.These results were supported by the reduction of the Cu lattice parameter and by the exothermic reactions,during differential scanning calorimetry(DSC)analysis,observed only in the samples subjected to ECAP processing.Aging heat treatment after ECAP processing promoted an additional hardening effect and the complete recuperation of the electrical conductivity,caused by the re-precipitation of the partially dissolved particles.The better combination of hardness(191 HV)and electrical conductivity(83.5%(IACS))was obtained after 4 ECAP passes at room temperature and subsequent aging at 380℃for 1 h.

Different role of second phase in the micro-galvanic corrosion of WE43 Mg alloy in NaCl and Na_(2)SO_(4) solution

Effect of the second phase in the micro-galvanic corrosion of a commercial Mg alloy containing rare earth elements, cast WE43 alloy,was investigated in 0.6 M NaCl solution and 0.6 M Na_(2)SO_(4)solution by scanning electron microscopy(SEM) observations, scanning Kelvin probe force microscopy(SKPFM) analysis, hydrogen evolution, weight loss measurement, and electrochemical techniques. It is confirmed that the second phase of cast WE43 alloy is more active than Mg matrix and exhibits an anodic role in the micro-galvanic corrosion with α-Mg matrix as cathode and dissolves preferentially in Na_(2)SO_(4)solution, in contrast to the situation in NaCl solution. The corrosion rate of cast WE43 alloy in Na_(2)SO_(4)solution is much higher than that in NaCl solution, which is different from the conventional wisdom and could be attributed to the different role of the second phase in the micro-galvanic corrosion in two solutions.

Phase-field study of the second phase particle effect on texture evolution of polycrystalline material

The second phase particle effect on texture evolution of polycrystalline material is studied through phase-field method. A unique field variable is introduced into the phase-field model to represent the second phase particles. Elastic interaction between particles and grains is also considered. Results indicate that in the presence of second phase particles the average particle diameter turns smaller than in the absence of these particles and retards texture formation by pinning effect. The second phase particles change the strain energy profile, which tremendously influences the pinning effect.

Effects of shape and size of second phase on mechanical properties of sintered Mo-Y_(2)O_(3) alloys

The morphology and size of second phase greatly influence the strengthening effect on oxidation dispersion strengthened Mo alloys.In this work,a novel nanostructuring strategy is adopted to modify the second phase of Y_(2)O_(3),and the corresponding effects of particle shape and size on mechanical properties of sintered Mo−Y_(2)O_(3) alloys were investigated.It is found that spherical particles with sizes below 200 nm are preferred due to the dominant intragranular distribution of second phases associated with better strengthening effect originating from dislocation pinning.With smaller particle size of Y_(2)O_(3) nanospheres(105 nm),the tensile strength of corresponding Mo alloy is enhanced by about 43.8%,much higher than that(8.3%)reinforced by second phase nanospheres with larger particle size(322 nm).Meanwhile,with similar particle size(around 100 nm),the spherical shape exhibits better strengthening effect than the one reinforced by one-dimensional rod-like second phase.

Monte Carlo study on abnormal growth of Goss grains in Fe-3%Si steel induced by second-phase particles

The selective abnormal growth of Goss grains in magnetic sheets of Fe-3%Si （grade Hi-B） induced by second-phase particles （AlN and MnS） was studied using a modified Monte Carlo Ports model. The starting microstructures for the simulations were generated from electron backscatter diffraction （EBSD） orientation imaging maps of recrystallized samples. In the simulation, second-phase particles were assumed to be randomly distributed in the initial microstructures and the Zener drag effect of particles on Goss grain boundaries was assumed to be selectively invalid because of the unique properties of Goss grain boundaries. The simulation results suggest that normal growth of the matrix grains stagnates because of the pinning effect of particles on their boundaries. During the onset of abnormal grain growth, some Goss grains with concave boundaries in the initial microstructure grow fast abnormally and other Goss grains with convex boundaries shrink and eventually disappear.

Grain growth simulation with the second phase particle pinning for heat-affected zone of microalloyed steel welds

The second phase particle dispersed in microalloyed steel has different effects on grain growth depending on their size and volume fiaction of the second phase particles which will change during welding thermal cycles. The particle coarsening and dissolution kinetics model was analyzed for continuous heating and cooling. In addition, based on experimental data, the coupled equation of grain growth was established by introducing limited size of grain growth with the consideration of the second phase particles pinning effects. Using Monte Carlo method based on experimental data model, the grain growth simulation for heat-affected zone of microalloyed steel welds was achieved. The calculating results were well in agreement with that of experiments.

Influence of Varying Crude Protein Levels and Balanced Amino Acids on the Performance and Haematological Characteristics of Laying Hens at the Second Phase of Production

Varying levels of dietary crude proteins and balanced amino acids were fed to layers for a period of eight weeks starting from the twenty-sixth week of age of birds and six weeks into egg production. Effects on performance and haematological characteristics were investigated at this second phase of production. Sixty Black Nera hens were randomly allotted into four (4) dietary treatments, containing the following levels of crude protein 14%, 15%, 16%, 17% and the metabolizable energy was iso-caloric for each treatment. The results showed that there were no significant differences (P > 0.05) observed for lymphocyte, Haemoglobin (Hb), Packed Cell Volume (PCV), Red Blood Cell (RBC) and White Blood Cell (WBC), these haematological parameters were within the range for healthy birds. Thus crude protein level of 14% can be used in diets of layers at the second phase of production provided that adequate amino acids are given, without adverse effect on egg laying, feed intake and measured blood parameters.

Effects of second phases on fracture behavior of Mg-10Gd-3Y-0.6Zr alloy

The effects of second phases on the fracture behavior of Mg-10Gd-3Y-0.6Zr alloy were investigated.The results show that the fracture mode can be generally described as ductile transgranular fracture in as-extruded condition and intergranular fracture in peak-aged condition.In as-extruded condition,the ductile transgranular fracture occurs by the formation and transgranular propagation of the microcrack from the broken primary phases.However,as the collaboration effects of precipitates inside grains and on the grain boundaries have the tendency to reduce the cohesive strength of the grain boundary,and make the grain boundaries the favorable path for crack propagation,the intergranular fracture occurs in peak-aged condition.

CALCULATION OF SECOND PHASE PARTICLE-GRAIN BOUNDARY INTERACTION RANGE

On the basis of the grain boundary equation by HeUman and corresponding analysis of Worner, this article deals with the interaction range between the second-phase particle （SPP） and grain boundary （GB） as viewed from the applicability of grain boundary equation. Also, a new expression describing the interaction range has been derived, which solves the problem in theory that the interaction range between SPP and GB can only be qualitatively analyzed previously. It is shown that given the interaction position between SPP and GB, the interaction range can be quantitatively determined by use of this expression.

Study protocol of the Asian XELIRI ProjecT(AXEPT):a multinational,randomized,non-inferiority,phase Ⅲ trial of second-line chemotherapy for metastatic colorectal cancer, comparing the eicacy and safety of XELIRI with or without bevacizumab versus FOLFIRI w

Background: Capecitabine and irinotecan combination therapy(XELIRI) has been examined at various dose levels to treat metastatic colorectal cancer(m CRC). Recently, in the Association of Medical Oncology of the German Cancer Society(AIO) 0604 trial, tri?weekly XELIRI plus bevacizumab, with reduced doses of irinotecan(200 mg/m^2 on day 1) and capecitabine(1600 mg/m^2 on days 1–14), repeated every 3 weeks, has shown favorable tolerability and eicacy which were comparable to those of capecitabine and oxaliplatin(XELOX) plus bevacizumab. The doses of capecit?abine and irinotecan in the AIO trial are considered optimal. In a phase I/II study, XELIRI plus bevacizumab(BIX) as second?line chemotherapy was well tolerated and had promising eicacy in Japanese patients.Methods: The Asian XELIRI Projec T(AXEPT) is an East Asian collaborative, open?labelled, randomized, phase Ⅲ clinical trial which was designed to demonstrate the non?inferiority of XELIRI with or without bevacizumab versus standard FOLFIRI(5?fluorouracil, leucovorin, and irinotecan combination) with or without bevacizumab as second?line chemo?therapy for patients with m CRC. Patients with 20 years of age or older, histologically conirmed m CRC, Eastern Coop?erative Oncology Group performance status 0–2, adequate organ function, and disease progression or intolerance of the irst?line regimen will be eligible. Patients will be randomized(1:1) to receive standard FOLFIRI with or with?out bevacizumab(5 mg/kg on day 1), repeated every 2 weeks(FOLIRI arm) or XELIRI with or without bevacizumab(7.5 mg/kg on day 1), repeated every 3 weeks(XELIRI arm). A total of 464 events were estimated as necessary to show non?inferiority with a power of 80% at a one?sided α of 0.025, requiring a target sample size of 600 patients. The 95% conidence interval(CI) upper limit of the hazard ratio was pre?speciied as less than 1.3.Conclusion: The Asian XELIRI Projec T is a multinational phase III trial being conducted to provide evidence for XELIRI with or without bevacizumab as a second?line treatment option of mCRC.

Phase-matched second-harmonic generation in hybrid polymer-LN waveguides

Here we propose a hybrid polymer-LN waveguide for achieving phase-matched second-harmonic generation(SHG).From the aspect of super-mode theory,the geometric parameters of the hybrid semi-nonlinear waveguide were optimized to utilize both symmetric(even)and antisymmetric(odd)modes of the pump and SHG waves so as to facilitate phase matching with large modal overlap.Phase matching between a fundamental even(TE_(00)-like)mode at 1320 nm and a fundamental odd(TE_(01)-like)mode at 660 nm was found with a calculated modal overlap integral of 0.299,while utilizing the largest nonlinear coefficient d_(33),and achieving an efficient calculated normalized conversion efficiency of 148%W^(-1)·cm^(-2).Considering the fabrication feasibility of such hybrid waveguide with features including etchless,large dimension,and low structural sensitivity,we believe our findings would provide a useful reference for future on-chip efficient nonlinear conversion devices.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

Understanding the catalytic performance and deactivation behaviour of second-promoter doped Pt/WO_(χ)/γ-Al_(2)O_(3) catalysts in the glycerol hydrogenolysis for selective and cleaner production of 1,3-propanediol

The selective aqueous-phase glycerol hydrogenolysis is a promising reaction to produce commercially useful 1,3-propanediol(1,3-PDO).The Pt-WOx bifunctional catalyst can catalyse the glycerol hydrogenol-ysis but the catalyst deactivation via sintering,metal leaching,and coking can predominantly occur in the aqueous phase reaction.In this work,the effect of reaction temperature,pressure and second promoter(Cu,Fe,Rh,Mn,Re,Ru,Ir,Sn,B,and P)on catalytic performance and deactivation behaviour of Pt/WOx/-Al2O3 was investigated.When doped with Rh,Mn,Re,Ru,Ir,B,and P,the second promoter boosts catalytic activity by promoting great dispersion of Pt on support and increasing Pt surface area.The increased Bronsted acid sites lead to selective synthesis of 1,3-PDO than 1,2-propanediol(1,2-PDO).The characterization studies of fresh and spent catalysts reveal that the main cause of catalyst deactivation is the Pt sintering,as interpreted based on XRD,CO chemisorption,and TEM analyses.The Pt sintering is affected depending on the second promoter that can either or reduce the interaction between Pt,WO_(χ)/γ and Al_(2)O_(3).As an electron acceptor of Pt in Pt/WO_(χ)/γ-Al_(2)O_(3),Re and Mn as second promoters resulted in increased Pt^(2+) on the catalytic surface,which strengthens the contact between Pt andγ-Al_(2)O_(3) and WO_(χ),resulting in a decrease in Pt sintering.The metal leaching and coking are not affected by the presence of second promoter.The catalyst modified with a second promoter possesses improved catalytic activity and 1,3-PDO production,however the stability continues to remain a challenge.The present work unrav-elled the determining parameters of catalytic activity and deactivation,thus providing a promising pro-tocol toward effective catalysts for glycerol hydrogenolysis.

EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.

Theoretical Study on the High-Temperature P6 and P6＇ Phases of Si3N4： A Tool to Aid in Ceramics Development

Atomistic modeling based on the density functional theory combined with the quasi-harmonic approximation is used to investigate the lattice parameters and elastic moduli of the P6 and P6＇ phases of Si3N4. β-Si3N4 is set as a benchmark system since accurate experiments are available. The calculated lattice constants and elastic constants of β-Si3N4 are in good agreement with the experimental data. The crystal anisotropy, mechanical stability, and brittle behavior of P6- and P6＇-Si3N4 are also discussed in the pressure range of 30-55 GPa. The results show that these two polymorphs are metallic compounds. The brittleness and elastic anisotropy increase with applied pressure increasing. Besides, the phase boundaries of the β→P6＇→δ transitions are also analysed. The β phase is predicted to undergo a phase transition to the P6＇ phase at 40.0 GPa and 300 K. Upon further compression, the P6＇→δ transition can be observed at 53.2 GPa. The thermal and pressure effects on the heat capacity, cell volume and bulk modulus are also determined. Some interesting features are found at high temperatures.

New theoretical analysis method for the phase center in the Fresnel region of complex structure antennas

A finite domain time difference （FDTD） and second-derivative combined method is proposed for the evaluation of phase center in the Fresnel region of complex structure millimeter antennas. This method adopts FDTD＇s near to far field transformation to obtain the fields in Fresnel region and then applies the second-derivative method to calculate the phase center. The adoption of FDTD efficiently overcomes the difficulties arising from the existing calculation methods＇ requirements for the radiation analytical formula of some complex antennas, which makes the existing second-derivative method more applicable in engineering. Also, FDTD increases the precision owing to the superposition field calculation from its extrapolation. The correctness of this proposed method is certified with typical examples and the phase center in the Fresnel region of a microwave radiometry calibration corrugate horn antenna is evaluated with the key features.