A New Theoretical Approach Based on the Maxwell Model to Obtain Rheological Properties of Solidifying Alloys and Its Val
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A. Historical Background
PREDICTION of cracking during casting, so-called ‘‘hot tearing’’ or ‘‘solidification cracking,’’ has recently attracted great interest.[1,2] Thermal stress analysis of casting requires the mechanical properties of alloys in partially solidified states. Experimental measurements of the properties have been taken and constitutive equations have been constructed.[3–13] Although the solidifying alloys are two-phase materials, they have been modeled as homogeneous continua to analysis at the macro scale. Solidifying alloys are known to show strain rate dependence of stress, or rheological behavior. AKIRA MATSUSHITA and RYOSUKE TAKAI are with the Department of Mechanical Engineering, Graduate School of Waseda University, 3-4-1 Shinjuku-ku Okubo, Tokyo 169-8555, Japan. Contact e-mail: [email protected] HIDEAKI EZAKI is with the Kubota Corporation, 2-47, Shikitsuhigashi 1-chome, Naniwaku, Osaka 556-8601, Japan. TOSHIMITSU OKANE is with the Advanced Manufacturing Research Institute, National Institute of Advanced Industrial Science and Technology, 1-1-1 Tsukuba Umezono, Ibaraki 305-8568, Japan. MAKOTO YOSHIDA is with the Department of Mechanical Engineering, Graduate School of Waseda University, and also with the Kagami Memorial Research Institute for Materials Science and Technology, Waseda University, 2-8-26 Shinjuku-ku Nishiwaseda, Tokyo, 169-0051, Japan. Manuscript submitted June 8, 2016. Article published online February 7, 2017 METALLURGICAL AND MATERIALS TRANSACTIONS A
Conventional methods used to obtain properties of this behavior are based on methods to obtain the steady state (secondary) creep properties of alloys below solidus.[3,14] Solidifying alloys show not only rheological but also brittle behavior, especially in the temperature range known as the brittle temperature range (BTR). Insufficient ductility of BTR alloys, meaning an absence of steady state stress in stress–strain curves, lead to difficulty in obtaining these properties using the conventional methods. B. Short-Comings of the Conventional Methods By the conventional methods using tensile,[3–6] share,[6–8] or compression[6,9–11] testing, the rheological properties such as stress exponent n and material consistent A in Norton’s law are obtained from relations between steady state stress and the total strain rate (logr log_etotal ) as presented in Figure 1(a). Total strain comprises elastic and inelastic (plastic and creep) strains. Here inelastic strain which causes strain hardening is called as plastic strain. Considering that elastic strain and plastic strain are both constant in the steady state, the total strain rate must be equal to the creep strain rate. Only in the case of a ductile state, this approach is available, because in a fragile state microscopic damage will inevitably occur before reaching the steady state. The tendency for the damage to occur is remarkable especially in tensile process. However, the mechanical properties used for analysis to predict hot tearing are VOLUME 48A, APRIL 2017—1701
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