Globularαphases can significantly improve the ductility of titanium alloys.Cyclic heat treatment(CHT)has been proved to be an effective way to induce the formation of globularαphases inα+βtitanium alloy Ti-6Al-4V ...Globularαphases can significantly improve the ductility of titanium alloys.Cyclic heat treatment(CHT)has been proved to be an effective way to induce the formation of globularαphases inα+βtitanium alloy Ti-6Al-4V fabricated by laser aided additive manufacturing(LAAM).However,there is no prior research reporting methods for obtaining globularαphases in LAAM-built near-αtitanium alloys.This work investigated the cyclic heat treatment(CHT)procedures suitable for the LAAM-built near-αtitanium alloy Ti-6Al-2Sn-4Zr-2Mo(Ti6242)to attain the globularαphases.The results show that 980℃ is the most suitable upper temperature limit for CHT.However,it is difficult to achieve a high volume fraction of the globularαphases in the LAAM-built Ti6242 alloys through CHT,which is ascribed to the low composition gradient caused by moreα-stabilizing elements and fewerβ-stabilizing elements.The as-built sample demonstrated elongation of 6.3%,which is lower than the AMS 4919J standard(elongation≥10%).After 980℃ CHT and 980℃ CHT with solution heat-treatment,the formation of the globularαphases significantly increased the elongation to 13.5%and 12.9%,respectively.Although the mechanical strength is reduced after heat-treatment,the room-temperature tensile properties still exceed the AMS 4919J standard.Fractography examination showed that the as-built sample exhibited a mixed brittle and ductile fracture behavior,while the 980℃ CHT and 980℃ CHT with solution heat-treated samples displayed ductile fracture.展开更多
We begin with the reference measure P0 induced by simple, symmetric nearest neighbor continuous time random walk on Zd starting at 0 with jump rate 2d and then define, for β≥0, t > 0, the Gibbs probability measur...We begin with the reference measure P0 induced by simple, symmetric nearest neighbor continuous time random walk on Zd starting at 0 with jump rate 2d and then define, for β≥0, t > 0, the Gibbs probability measure Pβ,t by specifying its density with respect to P0 as dPβ,t/dP0= Zβ,t（0）(-1eβ∫0tδ0（xs）ds),（0.1）where Zβ,t（0）≡E0[eβ∫<sup>t0δ0（xs）ds]. This Gibbs probability measure provides a simple model for a homopolymer with an attractive potential at the origin. In a previous paper（Cranston and Molchanov, 2007）, we showed that for dimensions d≥3 there is a phase transition in the behavior of these paths from the diffusive behavior for β below a critical parameter to the positive recurrent behavior for β above this critical value. The critical value was determined by means of the spectral properties of the operator ? + βδ0, where ? is the discrete Laplacian on Zd. This corresponds to a transition from a diffusive or stretched-out phase to a globular phase for the polymer. In this paper we give a description of the polymer at the critical value where the phase transition takes place. The behavior at the critical parameter is dimension-dependent.展开更多
基金supported by Agency for Science,Technology and Research(A∗Star),the Republic of Singapore,under the IAF-PP program‘Integrated large format hybrid manufacturing using wire-fed and powder-blown technology for LAAM process’(Grant No:A1893a0031).
文摘Globularαphases can significantly improve the ductility of titanium alloys.Cyclic heat treatment(CHT)has been proved to be an effective way to induce the formation of globularαphases inα+βtitanium alloy Ti-6Al-4V fabricated by laser aided additive manufacturing(LAAM).However,there is no prior research reporting methods for obtaining globularαphases in LAAM-built near-αtitanium alloys.This work investigated the cyclic heat treatment(CHT)procedures suitable for the LAAM-built near-αtitanium alloy Ti-6Al-2Sn-4Zr-2Mo(Ti6242)to attain the globularαphases.The results show that 980℃ is the most suitable upper temperature limit for CHT.However,it is difficult to achieve a high volume fraction of the globularαphases in the LAAM-built Ti6242 alloys through CHT,which is ascribed to the low composition gradient caused by moreα-stabilizing elements and fewerβ-stabilizing elements.The as-built sample demonstrated elongation of 6.3%,which is lower than the AMS 4919J standard(elongation≥10%).After 980℃ CHT and 980℃ CHT with solution heat-treatment,the formation of the globularαphases significantly increased the elongation to 13.5%and 12.9%,respectively.Although the mechanical strength is reduced after heat-treatment,the room-temperature tensile properties still exceed the AMS 4919J standard.Fractography examination showed that the as-built sample exhibited a mixed brittle and ductile fracture behavior,while the 980℃ CHT and 980℃ CHT with solution heat-treated samples displayed ductile fracture.
基金supported by National Science Foundation of USA (Grant Nos. DMS1007176 and DMS-0706928)
文摘We begin with the reference measure P0 induced by simple, symmetric nearest neighbor continuous time random walk on Zd starting at 0 with jump rate 2d and then define, for β≥0, t > 0, the Gibbs probability measure Pβ,t by specifying its density with respect to P0 as dPβ,t/dP0= Zβ,t（0）(-1eβ∫0tδ0（xs）ds),（0.1）where Zβ,t（0）≡E0[eβ∫<sup>t0δ0（xs）ds]. This Gibbs probability measure provides a simple model for a homopolymer with an attractive potential at the origin. In a previous paper（Cranston and Molchanov, 2007）, we showed that for dimensions d≥3 there is a phase transition in the behavior of these paths from the diffusive behavior for β below a critical parameter to the positive recurrent behavior for β above this critical value. The critical value was determined by means of the spectral properties of the operator ? + βδ0, where ? is the discrete Laplacian on Zd. This corresponds to a transition from a diffusive or stretched-out phase to a globular phase for the polymer. In this paper we give a description of the polymer at the critical value where the phase transition takes place. The behavior at the critical parameter is dimension-dependent.
