A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,co...A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,containing variational inequalities with nonlinear and nondifferentiable terms,are derived and studied.Existence,uniqueness and convergence results are obtained and shortly presented.A priori finite element error estimates are derived and an algorithm,combining the finite element and secant-modulus methods,is utilized to solve an illustrative extrusion problem.展开更多
Recently we have reported a number of bulk glass forming compositions in the CuHf-Ti system,with the critical thickness for complete glass formation,dc,ranging from 2 mm to 4 mm.In order to improve the glass forming a...Recently we have reported a number of bulk glass forming compositions in the CuHf-Ti system,with the critical thickness for complete glass formation,dc,ranging from 2 mm to 4 mm.In order to improve the glass forming ability （GFA） getting even larger dc,the prevailing approach is to use complex multicomponent systems.This strategy has been investigated by us for the Cu-Hf-Ti bulk glass forming alloy Cu55Hf25Ti20 using 〉1 at.pct additions of B,Y,Nb,Ta,Al,Mn,Si or V but with no significant improvement in the GFA.Clearly,it is necessary,in order to utilise the full potential of the base ternary system,to identify the best glass-forming compositions as a basis for extending the search into multi-dimensional compositional space.Thus,CuxHfyTiz alloys,where x=（40-70） at.pct,y=（5-30） at.pct,and z=（10-36） at.pct,were prepared by melt spinning andcopper mould suction-casting.The composition dependence of the GFA for the Cu-Hf-Ti alloys,as measured by dc for rod and ribbon samples,is reported over the composition range given above.展开更多
文摘A class of steady-state metal-forming problems,with rigid-plastic,incompressible,strain-rate dependent material model and nonlocal Coulomb’s friction,is considered.Primal,mixed and penalty variational formulations,containing variational inequalities with nonlinear and nondifferentiable terms,are derived and studied.Existence,uniqueness and convergence results are obtained and shortly presented.A priori finite element error estimates are derived and an algorithm,combining the finite element and secant-modulus methods,is utilized to solve an illustrative extrusion problem.
基金support of PAPIIT-UNAM IB100712SENER-CONACYT151496 in funding the project
文摘Recently we have reported a number of bulk glass forming compositions in the CuHf-Ti system,with the critical thickness for complete glass formation,dc,ranging from 2 mm to 4 mm.In order to improve the glass forming ability （GFA） getting even larger dc,the prevailing approach is to use complex multicomponent systems.This strategy has been investigated by us for the Cu-Hf-Ti bulk glass forming alloy Cu55Hf25Ti20 using 〉1 at.pct additions of B,Y,Nb,Ta,Al,Mn,Si or V but with no significant improvement in the GFA.Clearly,it is necessary,in order to utilise the full potential of the base ternary system,to identify the best glass-forming compositions as a basis for extending the search into multi-dimensional compositional space.Thus,CuxHfyTiz alloys,where x=（40-70） at.pct,y=（5-30） at.pct,and z=（10-36） at.pct,were prepared by melt spinning andcopper mould suction-casting.The composition dependence of the GFA for the Cu-Hf-Ti alloys,as measured by dc for rod and ribbon samples,is reported over the composition range given above.
