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Approximate Augmented lagrangian Functions and Nonlinear Semidefinite Programs

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Acta Mathematica Sinica,English Series 2006年第5期22卷 1283-1296页

作者： x.x.HUANG K.l.TEO x.q.YANG School of Management Fudan University Shanghai 200433 P. R. China and Department of Mathematics and Computer Science Chongqing Normal UniversityChongqing 400047 P. R. China Department of Mathematics and Statistics Curtin University of Technology Perth Australia Department of Applied Mathematics The Hong Kong Polytechnic UniversityKowloon Hong Kong P. R. China

In this paper, an approximate augmented lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented lagrangian problems converges to a solution of the original semidefinite program.

关键词： semidefinite programming augmented lagrangian duality exact penalty convergence,stationary point

A SIMUlATION STUDY OF DEPOSITION UNDER TWO TYPES OF IMPINGING TRAJECTORIES

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Acta Metallurgica Sinica(English letters) 2004年第6期17卷 876-880页

作者： x.q.Wei l.Zhou SchoolofMaterialsScience＆Engineering NanchangUniversityNanchang330047China

A model coupling particle aggregation and randomwalk surface diffusion has been developed for 2D simulation of depositional growth, in which impinging particles follow either a straight-line trajectory of cosine distribution, representing typically sputter deposition, or a scattered trajectory, representing typically electrochemical deposition. Simulations of the growth under various impinging conditions and effective surface diffusivity have been carried out. Pattern and defect development in deposition on flat, trenched and ridged substrates have been investigated. We found that on flat and ridged substrates, both types of trajectories yield similar features, including formation of cone-like defects on surface ridges. While on trenched substrate, the straight-line impingement yielded more uniform step coverage than the scattered impingement.

关键词： deposition simulation pattern formation ballistic model

Stability analyses of the mass abrasive projectile high-speed penetrating into a concrete target Part III: Terminal ballistic trajectory analyses

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Acta Mechanica Sinica 2015年第4期31卷 558-569页

作者： H.Wu x.W.Chen q.Fang x.Z.Kong l.l.He Institute of Systems Engineering China Academy of Engineering Physics State Key laboratory for Disaster Prevention & Mitigation of Explosion & Impact PLA University of Science and Technology

During the high-speed penetration of projectiles into concrete targets （the impact velocity ranges from 1.0 to 1.5 km/s）, important factors such as the incident oblique and attacking angles, as well as the asymmetric abrasions of the projectile nose induced by the target-projectile interactions, may lead to obvious deviation of the terminal ballistic tra- jectory and reduction of the penetration efficiency. Based on the engineering model for the mass loss and nose-blunting of ogive-nosed projectiles established, by using the Differ- ential Area Force law （DAFl） method and semi-empirical resistance function, a finite differential approach was pro- grammed （PENTRA2D） for predicting the terminal ballistic trajectory of mass abrasive high-speed projectiles penetrating into concrete targets. It accounts for the free-surface effects on the drag force acting on the projectile, which are attributed to the oblique and attacking angles, as well as the asymmetric nose abrasion of the projectile. Its validation on the prediction of curvilinear trajectories of non-normal high-speed pene- trators into concrete targets is verified by comparison with available test data. Relevant parametric influential analyses show that the most influential factor for the stability of ter- minal ballistic trajectories is the attacking angle, followed by the oblique angle, the discrepancy of asymmetric nose abrasion, and the location of mass center of projectile. The terminal ballistic trajectory deviations are aggravated as the above four parameters increase.

关键词： Projectile Penetration Concrete Massabrasion Terminal ballistic trajectory

Spalling characteristics of high-temperature treated granitic rock at different strain rates

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第4期16卷 1280-1288页

作者： l.F.Fan q.H.Yang x.l.Du The Key laboratory of Urban Security and Disaster Engineering of Ministry of Education Beijing University of TechnologyBeijing100124China

The dynamic spalling characteristics of rock are important for stability analysis in rock *** paper presented an experimental investigation on the dynamic spalling characteristics of granite with different temperatures and strain rates.A series of dynamic spalling tests with different impact velocities were conducted on thermally treated granite at different *** dynamic spalling strengths of granite with different temperatures and strain rates were determined.A model was proposed to correlate the dynamic spalling strength of granite,high temperature and strain *** results show that the spalling strength of granite decreases with increasing ***,the spalling strength of granite with a higher strain rate is larger than that with a lower strain *** proposed model can describe the relationship among dynamic spalling strength of granite,high temperature and strain rate.

关键词： Dynamic spalling characteristics High temperature Strain rate Dynamic loading Granite

In situ TEM investigation of electron irradiation and aging-induced high-density nanoprecipitates in an Mg-10Gd-3Y-1Zn-0.5Zr alloy

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Journal of Magnesium and Alloys 2024年第5期12卷 1841-1853页

作者： M.lv H.l.Ge q.q.Jin x.H.Shao Y.T.Zhou B.Zhang x.l.Ma Shenyang National laboratory for Materials Science Institute of Metal ResearchChinese Academy of Sciences72 Wenhua RoadShenyang 110016China School of Materials Science and Engineering University of Science and Technology of ChinaShenyang 110016China Materials Science and Engineering Research Center Guangxi University of Science and TechnologyLiuzhou 545006China

In-situ electron irradiation and aging are applied to introduce high-density precipitates in an Mg-10Gd-3Y-1Zn-0.5Zr(GWZ1031K,wt.%)alloy to improve the *** results show that the hardness of the Mg alloy after irradiation for 10 h and aging for 9 h at 250℃ is 1.64 GPa,which is approximately 64% higher than that of the samples before being *** is mainly attributed to γ'precipitates on the basal plane after irradiation and the high-density nanoscale β'precipitates on the prismatic plane after aging,which should be closely related to the irradiation-induced homogenous *** latter plays a key role in precipitation *** result paves a way to improve the mechanical properties of metallic materials by tailoring the precipitation through irradiation and aging.

关键词： Mg alloy Electron beam irradiation Hardening Precipitates In-situ TEM

Effect of grain size on fatigue cracking at twin boundaries in a CoCrFeMnNi high-entropy alloy

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Journal of Materials Science & Technology 2020年第4期39卷 1-6页

作者： A.G.Wang x.H.An J.Gu x.G.Wang l.l.li W.l.li M.Song q.q.Duan Z.F.Zhang x.Z.liao School of Aerospace Mechanical&Mechatronic EngineeringThe University of Sydne0ySydneyAustralia State Key laboratory of Powder Metallurgy Central South UniversityChangsha 410083China Materials Fatigue and Fracture Division Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China Max-Planck-Institut für Eisenforschung Max-Planck-Stra?e 140237 DüsseldorfGermany

The fatigue cracking behavior at twin boundaries(TBs)in a Co Cr Fe Mn Ni high-entropy alloy with three different grain sizes was systematically investigated under low-cycle *** of grain size,the change from slip band cracking to TB cracking occurred with increasing the difference in the Schmid factors(DSF)between matrix and ***,the required critical DSF for the transition of the dominant cracking mode decreases with decreasing grain size due to the reduced slip band spacing that increases the impingement sites on the TBs and facilitates the coalescence of defects and voids to initiate TB cracks.

关键词： High-entropy alloy Fatigue cracking Twin boundary Slip band Grain size

Role of extrusion rate on the microstructure and tensile properties evolution of ultrahigh-strength low-alloy Mg-1.0Al-1.0Ca-0.4Mn(wt.%)alloy

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Journal of Magnesium and Alloys 2023年第2期11卷 553-561页

作者： x.q.liu x.G.qiao R.S.Pei Y.q.Chi l.Yuan M.Y.Zheng School of Material Science and Engineering Harbin Institute of TechnologyHarbin 150001China Institut fur Metallkunde und Meterialphysik RWTH Aachen UniversityAachen D-52056Germany

Mg-1.0Al-1.0Ca-0.4Mn(AxM1104, wt.%) low alloy was extruded at 200 ℃ with an extrusion ratio of 25 and different ram speeds from 1.0 to 7.0 mm/s. The influence of extrusion rate on microstructure and mechanical properties of the AxM1104 alloy was systematically studied. With the increasing of extrusion rate, the mean dynamically recrystallized(DRxed) grain size of the low alloy and average particles diameter of precipitate second phases were increased, while the degree of grain boundary segregation and the intensity of the basal fiber texture were decreased. With the rising of extrusion rate from 1.0 to 7.0 mm/s, the tensile yield strength(TYS) of the as-extruded AxM1104 alloy was decreased from 445 MPa to 249 MPa, while the elongation to failure(El) was increased from 5.0% to 17.6%. The TYS, ultimate tensile strength(UTS) and El of the AxM1104 alloy extruded at the ram speed of 1.5 mm/s was 412 MPa, 419 MPa and 12.0%, respectively,exhibiting comprehensive tensile mechanical properties with ultra-high strength and excellent plasticity. The ultra-high TYS of 412 MPa was mainly due to the strengthening from ultra-fine DRxed grains with segregation of solute atoms at grain boundaries. The strain hardening rate is increase slightly with increasing extrusion speed, which may be ascribed to the increasing mean DRxed grain size with rising extrusion speed. The higher strain hardening rate contributes to the higher El of these AxM1104 samples extruded at higher ram speed.

关键词： Mg-Al-Ca-Mn alloy Ultrafine grain Extrusion rate Grain boundary segregation Microstructure Ultrahigh strength

Formation of β' phase in lPSO structures in an Mg88Co5Y7 alloy

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Journal of Magnesium and Alloys 2022年第1期10卷 175-182页

作者： q.q.Jin x.H.Shao Y.T.Zhou B.Zhang S.J.Zheng x.l.Ma Shenyang National laboratory for Materials Science Institute of Metal ResearchChinese Academy of Sciences72 Wenhua Road110016 ShenyangChina Materials Science and Engineering Research Center Guangxi University of Science and TechnologyLiuzhou 545006China School of Materials Science and Engineering Research Institute for Energy Equipment MaterialsHebei University of TechnologyTianjin 300130China

Formation of β’ phase in long-period stacking ordered(lPSO) structures in an Mg;Co;Y;(at.%) alloy after aging at 200 °C for 24 h or electron beam(EB) irradiation has been studied by high-angle annular dark-field scanning transmission electron microscopy(HAADFSTEM). β’ phase was precipitated only in the Mg matrix but not in lPSO structures after aging at 200 °C for 24 h. lPSO structure containing stacking defects transforms into the β’-long phase during EB irradiation, which plays a key role in accelerating solute atoms’ diffusion. New complex β’(lPSO) structures formed in the alloy after EB irradiation, such as β’(12 H) structure with an orthorhombic lattice(Mg;Y, Cmcm,a = 2 _(a0)= 0.642 nm, b=4√3_(a0), c = 6 _(c0)= 3.12 nm).

关键词： Magnesium alloys long-period stacking ordered(lPSO)structure HAADF-STEM β’phase

Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy

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Journal of Materials Science & Technology 2022年第24期119卷 11-24页

作者： W.l.Wang W.q.liu x.Yang R.R.xu q.Y.Dai School of Metallurgical Engineering Xi’an University of Architecture and TechnologyXi’an 710055China

A model of coupling macro finite volume method(FVM) and cellular automata(CA) is proposed in this paper to explore the columnar-to-equiaxed transition(CET) during selective laser melting(SlM) of rare earth magnesium *** into account the impact of recoil pressure and Marangoni convection on the molten pool temperature field,the grain structure is *** suggested by the simulation results,with the undissolved Zr serving as heterogeneous nucleation sites,the liquid undercooled layer under the combined action of forced cooling,the temperature gradient and the liquid solute concentration gradient leads to *** considering the dissolution of Zr in magnesium matrix,the results demonstrate that the dissolution of element Zr is effective in significantly inhibiting the growth of columnar crystals and ensuring the sufficient constitutional supercooling(CS) required for *** addition,to raise the preheating temperature contributes to enhancing the outcome of nucleation and incresing the grain *** the interdependence model(IM),with the cooling rate gradually increasing in the SlM process of magnesium alloy,the nucleation-free zone(NFZ) reduces by decreasing the solute diffusion layer in the front of the solid/liquid(Sl) interface and the temperature *** reduction in temperature gradient can promote undercooling for nucleation and facilitate the development of equiaxed *** simulation results are qualitatively verified as highly consistent through experimentation.

关键词： Multi-scale simulation Columnar-to-equiaxed transition Selective laser melting Rare earth magnesium alloy Constitutional supercooling