Thermal-tempering analysis of bulk metallic glass plates using an instant-freezing model
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. INTRODUCTION
ALTHOUGH metallic glasses have been made since the 1960s, specimen dimensions were previously limited to tens of microns, due to the very fast cooling rates (about 106 to 1012 K/s) needed in order to prevent crystallization. Recently, multicomponent alloys with an exceptional glassformation ability have been developed, allowing the processing of bulk specimens.[1] These alloys form glass at critical cooling rates low enough to allow the casting of specimens up to 10 cm in diameter. The ability to prepare large specimens has permitted the bulk characterization of these materials using more traditional techniques. The unique properties of bulk metallic glasses (BMGs) potentially place them among significant engineering materials: a very high strength (1.9 GPa) and fracture toughness (20 to 55 MPa ⭈ m1/2), a near-theoretical specific strength, excellent wear and corrosion resistance, and a high elastic strain limit (about 2 pct).[2,3] As with other materials, residual stresses can affect the mechanical behavior of BMGs significantly. One source for such stresses is thermal tempering. This is a process that forms a usually favorable residual-stress profile in materials of viscoelastic nature at high temperatures. It is commonly observed in silicate-based glasses and has been an industrial process for about 100 years.[4] Thermal tempering involves heating glass above its glass transition temperature (Tg) and then rapidly quenching it. During quenching, the surfaces of a glass plate solidify and contract first, leading to tension on the surface and compression in the midplane. The same would occur in an elastic solid. However, in this phase of quenching a glass, the core is still relatively fluid (i.e., of low viscosity) and the midplane compressive stresses are simultaneously relaxed by viscous flow. Thus, stresses developed before the entire cross section solidifies are lower than those in an C.C. AYDINER, Graduate Student, Department of Applied Mechanics, ¨ STU ¨ NDAG ¯ , Assistant Professor, and J.C. HANAN, Graduate and E. U Student, Department of Materials Science, are with the Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125. Manuscript submitted January 17, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
otherwise identical but elastic material with the same temperature distribution. However, when the midplane finally solidifies, the viscous effects cease and the material becomes practically an elastic glass plate, imposed with the temperature profile at that instant. All further changes in stresses are determined by the changes in the temperature profile only. As the temperature gradients decay to a constant value at room temperature, stresses in the opposite sense are produced: tension in the midplane and compression on the surface. For an always elastic solid, these would be equal and opposite to those produced in the first phase when temperature gradients grew. In a glass, which involves stress relaxation at the beginning, these are not equal.
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