Niyama

Prediction of Shrinkage Pore Volume Fraction Using a Dimensionless Niyama Criterion
KENT D. CARLSON and CHRISTOPH BECKERMANN A method is presented to use a dimensionless form of the well-known Niyama criterion to directly predict the amount of shrinkage porosity that forms during solidification of metal alloy castings. The main advancement offered by this method is that it avoids the need to knowthe threshold Niyama value below which shrinkage porosity forms; such threshold values are generally unknown and alloy dependent. The dimensionless criterion accounts for both the local thermal conditions (as in the original Niyama criterion) and the properties and solidification characteristics of the alloy. Once a dimensionless Niyama criterion value is obtained from casting simulation results,the corresponding shrinkage pore volume fraction can be determined knowing only the solid fraction-temperature curve and the total solidification shrinkage of the alloy. Curves providing the shrinkage pore volume percentage as a function of the dimensionless Niyama criterion are given for WCB steel, aluminum alloy A356, and magnesium alloy AZ91D. The present method is used in a general-purposecasting simulation software package to predict shrinkage porosity in three-dimensional (3-D) castings. Comparisons between simulated and experimental shrinkage porosity results for a WCB steel plate casting demonstrate that this method can reasonably predict shrinkage. Additional simulations for magnesium alloy AZ91D illustrate that this method is applicable to a wide variety of alloys and castingconditions. DOI: 10.1007/s11661-008-9715-y Ó The Minerals, Metals & Materials Society and ASM International 2008

I.

INTRODUCTION
[1]

THE Niyama criterion is presently the most widely used criterion function in metal casting. It is used to predict feeding-related shrinkage porosity caused by shallow temperature gradients. All casting simulation software packages calculate the Niyama criterionas a standard output; foundries worldwide use this criterion to predict the presence of shrinkage in castings. Foundry-simulation users view Niyama contour plots predicted by a casting simulation and expect that shrinkage porosity will form in regions that contain Niyama values below some threshold value. The Niyama criterion is a local thermal parameter defined as .pffiffiffiffi _ Ny ¼ G T ½1Š
_ where Gis the temperature gradient and T is the cooling rate, both of which are evaluated at a specified temperature near the end of solidification. Niyama et al.[1] empirically determined the functional form of this criterion, but they also offered a physical model as justification. The model begins with Darcy’s law, which relates the interdendritic feeding-flow velocity to the pressure drop across themushy zone. By making simplifying assumptions about the functional form of

KENT D. CARLSON, Research Engineer, and CHRISTOPH BECKERMANN, Professor, are with the Department of Mechanical and Industrial Engineering, The University of Iowa, Iowa City, IA 52242. Contact e-mail: becker@engineering.uiowa.edu Manuscript submitted July 28, 2008. Article published online November 26, 2008
METALLURGICAL ANDMATERIALS TRANSACTIONS A

the solid fraction-temperature curve and the permeability, they were able to analytically integrate the onedimensional (1-D) form of Darcy’s law to demonstrate  _ that DP / T G2 (or DP / NyÀ2 ), where DP is the pressure drop across the mushy zone. By comparing experimentally observed shrinkage porosity patterns in cast-steel cylinders to corresponding castingsimulations, Niyama et al. discovered that there was a threshold value of Ny below which shrinkage was typically present. While the presence of the temperature gradient in Eq. [1] is not surprising, and implies that shrinkage porosity will form in regions of low G, the presence of the cooling rate (albeit inside a square root) in the denominator may at first seem counterintuitive. The Niyama criterion...