• PDF / 2,076,332 Bytes
• 17 Pages / 598.28 x 778.28 pts Page_size
• 47 Downloads / 205 Views

DOWNLOAD

REPORT

---

I.

INTRODUCTION

SOLIDIFICATION modeling has been used to aid in the location of feeding sprues, gates, runners, and risers, along with the orientation of the casting, and the selection of process variables such as pouring temperature and mold materials to eliminate porosity and cold shuts and to predict residual stresses. ~ While lack of integrity of the casting accounts for a significant percentage of scrap, failure to meet microstructural and mechanical specifications is also an expensive problem. As an aid to solving these types of problems, microstructure models that track the nucleation and growth of the microstructure in a solidification simulation have been developed. One of the casting alloys which will benefit greatly from microstructure modeling is gray iron. The phases which will form during solidification are determined by the composition of the iron, the relative abundance of various nucleation sites, and how rapidly the metal is solidified. Cast irons may solidify in either the rectastable Fe-Fe3C system or the stable Fe-C system, or in both. The austenite matrix can transform to pearlite, ferrite, or both. This competition between phases complicates the modeling of microstructure development in these alloys. In Sections B-1 through B-4, the kinetics of formation of each of the different microstructures will be discussed in detail. However, we wish to discuss them in the context of inclusion in a macroscopic heattransfer code, so this will be discussed first. Macroscopic heat-flow modeling has become a wellstudied subject, and we therefore confine our discussion to that necessary for understanding microstructural modeling. The transient heat-conduction equation is solved in the solidifying iron and in the mold, viz.

dh P dt

- - = V.(kVT)

[1]

DAVID D. GOETTSCH, formerly Research Assistant, University of Illinois. is Senior Project Engineer, GM Powertrain Division, General Motors Corporation, Casting Technology Center, Saginaw, MI 48605-50730. JONATHAN A. DANTZIG, Associate Professor, is with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801. Manuscript submitted April 13, 1993. METALLURGICALAND MATERIALSTRANSACTIONS A

where p is the density, h is the specific enthalpy, t is time, k is thermal conductivity, and T is the temperature. The enthalpy change may be written in terms of the sensible heat and the heat of transformation as dh --

dt

dr =

--

cp dt

+

L

dt

[2]

where cp is the specific heat, L is the latent heat of the transformation, andfis the volume fraction transformed. In conventional macroscopic modeling, the specific enthalpy is assumed to be a known function of temperature, determined from a phase diagram or a solidification model. Thus, Eq. [2] may be rewritten as

%+L

--;7 = 4 ff

[3]

Once appropriate boundary conditions are specified, Eq. [ 1] may be solved for the transient temperature field, typically using either a finite-difference or finite-element method. When modeling microstructural development, however, the evolution