Modeling stress development during the solidification of gray iron castings
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I.
INTRODUCTION
IN general,
the design of a new cast part is still accomplished through the time-honored method of hand-drawn blueprints, prototyping, and redesign. In order to reduce the expense of this approach, it is desirable to design and evaluate new products on the computer rather than go directly to prototype development. Part of this evaluation involves simulating the heat transfer and thermal stress evolution as the casting solidifies and cools. Methods for obtaining the thermal history were the subject of previous work by the present authors tl-4] as well as many other researchers, f51 In our work, techniques were developed to eliminate solution of the heat transfer problem in the mold by applying instead a set of boundary conditions to the surface of the casting. These boundary conditions were selected by comparing the local part geometry to those precalculated and stored in a library of candidate boundary conditions. A similar approach was taken for the stress problem: a new boundary condition element was developed to provide the mechanical restraints normally exerted by the mold, eliminating the need to enmesh the mold itself. When computing the stresses associated with the casting process, proper account must be taken for the mechanical behavior of cast iron. t6] Because the microstructure of gray iron consists of a matrix of steel containin~ flakes of graphite, the material has very different properties in tension than it does in compression. Under compression, the flakes are held tightly closed, and the bulk material acts very much like steel, though somewhat weaker. Under tension, the flakes bear almost no load, reducing the effective load-bearing area and sometimes acting as stress concentrators. Figure 1 shows JEFFREY W. WIESE, formerly at the University of Illinois, is Process Engineer with Reynolds Metals Company, Richmond, VA 23261. JONATHAN A. DANTZIG, Associate Professor, is with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801. Manuscript submitted April 26, 1989. METALLURGICAL TRANSACTIONS A
the room-temperature tension and compression properties for a typical gray cast iron. In this case, the ratio of compressive strength to tensile strength is approximately 2: 1, but it is often greater and could be as high as 5:1 .t61 This paper describes a proper representation for the yield surface of gray iron and methods for its incorporation into a finite element analysis. The formulation was incorporated in a commercial code, ANSYS. t7,81
II.
METHODS AND RESULTS
A. Cast Iron Plasticity Element In 1976, Frishmuth and McLaughlin examined the failure of cast irons by performing a limit analysis on a "representative volume element" of cast iron.t91 For gray cast iron, the representative volume element was a single eutectic cell, idealized as a cube with cracks (or slits) radiating from the center. The matrix material was assumed to follow the yon Mises yield condition, and the slits were assumed to be rough and to have a very small distance betw
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