• Transactions of Materials Processing
• /
• v.14 no.4 s.76
• /
• pp.384-391
• /
• 2005

The nickel-based alloy Nimonic 80A possesses the excellent strength, and the resistance against corrosion, creep and oxidation at high temperature. Its products are used in aerospace engineering, marine engineering and power generation, etc. Control of forging parameters such as strain, strain rate, temperature and holding time is important because change of the microstructure in hot working affects the mechanical properties. Change of the microstructure evolves by recovery, recrystallization and grain growth phenomena. The dynamic recrystallization evolution has been studied in the temperature range of $950\~1250^{\circ}C$ and strain rate range of $0.05\~5s^{-1}$ using hot compression tests. The metadynamic recrystallization and grain growth evolution has been studied in the temperature range of $950\~1250^{\circ}C$ and strain rate range $0.05,\;5s^{-1}$, holding time range of 5, 10, 100, 600 sec using hot compression tests. Modeling equations are proposed to represent the flow curve, recrystallized grain size, recrystallized fraction and grain growth phenomena by various tests. Parameters in modeling equations are expressed as a function of the Zener-Hollomon parameter. The modeling equation for grain growth is expressed as a function of the initial grain size and holding time. The modeling equations developed were combined with thermo-viscoplastic finite element modeling to predict the microstructure change evolution during hot forging process. The grain size predicted from FE simulation results is compared with results obtained in field product.

• East Asian mathematical journal
• /
• v.10 no.2
• /
• pp.313-327
• /
• 1994

• East Asian mathematical journal
• /
• v.10 no.1
• /
• pp.123-133
• /
• 1994

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.505-516
• /
• 2001

We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: ${\upsilon}"(t)-M(｜{\nablauu}(t)｜^2){\triangle}u(t)-{\delta}{\triangle}u'(t)=f(t)$. As an application, a Kirchhoff model with viscosity is given.

• Journal of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1123-1139
• /
• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.27-40
• /
• 2017

In this paper, we construct exact traveling wave solutions of various kind of partial differential equations arising in mathematical science by the system technique. Further, the $Painlev{\acute{e}}$ test is employed to investigate the integrability of the considered equations. In particular, we describe the behaviors of the obtained solutions under certain constraints.

• Journal of Applied and Pure Mathematics
• /
• v.6 no.1_2
• /
• pp.71-96
• /
• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.9
• /
• pp.90-100
• /
• 1997

A full three-dimensional thermo-coupled rigid-viscoplastic finite element method and the currently developed microstructural evolution system which includes semi-empirical equations suggested by different research groups were used together to form an integrated system of process and micro- structure simulation of hot rolling. The distribution and time histroy of the momechanical variables such as temperature, strain, strain rate, and time during pass and between passes were obtained from the finite element analysis of multipass hot rolling processes. The distribution of metallurgical variables were calculated on the basis of instantaneous thermomechanical data. For the verification of this method the evolution of microstructure in plate rolling and shape rolling was simulated and their results were compared with the data available in the literature. Consequently, this approach makes it possible to describe the realistic evolution of microstructure by avoiding the use of erroneous average value and can be used in CAE of multipass hot rolling.

• Journal for History of Mathematics
• /
• v.24 no.1
• /
• pp.31-44
• /
• 2011

Partial differential equations on a Riemannain manifold is one of the most important areas in differential geometry. In this article, we survey the role of parabolic equations on some of the main results of differential geometry and topology, especially in the modern mathematical history. Also, we introduce some recent research in this area.

• Proceedings of the Korea Institute of Fire Science and Engineering Conference
• /
• 1997.11a
• /
• pp.112-119
• /
• 1997

The modelling of carbon substances obtaining, for instance, carbon fibers which have high fire resistance, has been realized on the example of the polyacrylonitrile pyrolysis modelling. The pyrolysis is considered as a double step process when the formation of a liquid phase and the oxidation of substance are excluded. Three main reactions are considered: a) with the evolution of ammonia; b) with the evolution of hydrogen cyanide; c) with the evolution of hydrogen. Reactions b) and c) are sequential, and a) and b) are parallel. The problem is formulated as one-dimensional. The equations of energy, masses or concentrations, porosity and thermal conductivity are proposed. The mathematical model of the carbonization process is designed using tile kinetic characteristics of the above reactions and the thermodynamic parameters of reagents and products in these reactions. The equations received are calculated by Runge-Cutta method and by Adams method of the fourth order accuracy.