Estimating the rank of a beta matrix: a GMM approach1

2019 ◽  
Vol 60 (4) ◽  
pp. 4147-4173
Author(s):  
Yu Ren ◽  
Qin Wang
Keyword(s):  
Beta Matrix

Decomposition of the metastable beta titanium alloy Ti-15-3

1983 ◽  
Vol 41 ◽  
pp. 264-265
Author(s):  
Y. L. Chen ◽  
S. Fujlshiro
Keyword(s):  
Low Cost ◽  
High Strength ◽  
Alpha Phase ◽  
Thick Sheet ◽  
Omega Phase ◽  
Beta Titanium Alloy ◽  
Beta Titanium ◽  
Beta Matrix ◽  
Metastable Beta ◽  
Very High

Metastable beta titanium alloys have been known to have numerous advantages such as cold formability, high strength, good fracture resistance, deep hardenability, and cost effectiveness. Very high strength is obtainable by precipitation of the hexagonal alpha phase in a bcc beta matrix in these alloys. Precipitation hardening in the metastable beta alloys may also result from the formation of transition phases such as omega phase. Ti-15-3 (Ti-15V- 3Cr-3Al-3Sn) has been developed recently by TIMET and USAF for low cost sheet metal applications. The purpose of the present study was to examine the aging characteristics in this alloy.The composition of the as-received material is: 14.7 V, 3.14 Cr, 3.05 Al, 2.26 Sn, and 0.145 Fe. The beta transus temperature as determined by optical metallographic method was about 770°C. Specimen coupons were prepared from a mill-annealed 1.2 mm thick sheet, and solution treated at 827°C for 2 hr in argon, then water quenched. Aging was also done in argon at temperatures ranging from 316 to 616°C for various times.

Ultra-Fine Grained Ti-15Mo Alloy Prepared by Powder Metallurgy

2018 ◽  
Vol 941 ◽  
pp. 1276-1281
Author(s):  
Anna Terynková ◽  
Jiří Kozlík ◽  
Kristína Bartha ◽  
Tomáš Chráska ◽  
Josef Stráský
Keyword(s):  
Powder Metallurgy ◽  
Bulk Material ◽  
Alpha Phase ◽  
Full Density ◽  
Fine Grained ◽  
Cryogenic Milling ◽  
Aircraft Manufacturing ◽  
Plasma Sintering ◽  
Beta Matrix ◽  
Spark Plasma

Ti-15Mo alloy belongs to metastable β-Ti alloys that are currently used in aircraft manufacturing and Ti15Mo alloy is a perspective candidate for the use in medicine thanks to its biotolerant composition. In this study, Ti15Mo alloy was prepared by advanced techniques of powder metallurgy. The powder of gas atomized Ti-15Mo alloy was subjected to cryogenic milling to achieve ultra-fine grained microstructure within the powder particles. Powder was subsequently compacted using spark plasma sintering (SPS). The effect of cryogenic milling on the microstructure and phase composition of final bulk material after SPS was studied by scanning electron microscopy. Sintering at 750°C was not sufficient for achieving full density in gas atomized powder, while milled material could be successfully sintered at this temperature. Alpha phase particles precipitated during sintering and their size, as well as the size of beta matrix grains, was strongly affected by the sintering temperature.

scholarly journals PRELIMINARY INVESTIGATION OF BILLET PROCESSING ROUTE ON MICROSTRUCTURE, TEXTURE AND FATIGUE RESPONSE OF Ti834 FORGED DISC PRODUCTS

2020 ◽  
Vol 321 ◽  
pp. 11031
Author(s):  
B. Fernandez-Silva ◽  
B. P. Wynne ◽  
M. Jackson ◽  
M. Bodie ◽  
K. Fox
Keyword(s):  
Fatigue Life ◽  
Texture Analysis ◽  
Fatigue Fracture ◽  
Thermomechanical Processing ◽  
Preliminary Investigation ◽  
Processing Route ◽  
Bimodal Microstructure ◽  
Primary Alpha ◽  
Dwell Fatigue ◽  
Beta Matrix

Non-standard processing routes for the manufacture of industrial scale Ti834 billet have been undertaken to investigate their effect on macrozones in final forged product. Microstructure, texture and dwell fatigue fracture surfaces were characterised from forged disc samples fabricated from these new billets. All processing routes showed a bimodal microstructure consisting of 25pct of primary alpha grains in a transformed beta matrix. Texture analysis has revealed variations in the presence and size of macrozones with relatively weak textures. Quasi-cleavage facets were present in all dwell fatigue samples although the fatigue life was doubled for the sample whose thermomechanical processing has the highest imposed strain.

Distributions of powers of the central beta matrix variates and applications

2019 ◽  
Vol 29 (3) ◽  
pp. 651-668
Author(s):  
Thu Pham-Gia ◽  
Duong Thanh Phong ◽  
Dinh Ngoc Thanh
Keyword(s):  
Beta Matrix

Beta Matrix and Common Factors in Stock Returns

2018 ◽  
Vol 53 (3) ◽  
pp. 1417-1440 ◽  
Author(s):  
Seung C. Ahn ◽  
Alex R. Horenstein ◽  
Na Wang
Keyword(s):  
Stock Returns ◽  
Common Factors ◽  
Information Criterion ◽  
Full Column Rank ◽  
Estimation Methods ◽  
Pricing Models ◽  
Risk Premiums ◽  
Multifactor Model ◽  
Asset Pricing Models ◽  
Beta Matrix

We consider the estimation methods for the rank of a beta matrix corresponding to a multifactor model and study which method would be appropriate for data with a large number of assets. Our simulation results indicate that a restricted version of Cragg and Donald’s (1997) Bayesian information criterion estimator is quite reliable for such data. We use this estimator to analyze some selected asset pricing models with U.S. stock returns. Our results indicate that the beta matrix from many models fails to have full column rank, suggesting that risk premiums in these models are underidentified.

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