A Fast Spreadsheet Model for the Yield Strength of Superalloys

Abstract

Simulation methods allow the possibility of overcoming some of the deficiencies of analytical models. In a recent work, we have developed a numerical model (the details of which are published elsewhere 7 ) that considers the actual microstructure of a superalloy and uses accurate descriptions of dislocation behavior to predict the critical resolved shear stress for a given microstructure. This numerical model captures the physics of the problem accurately (for cutting via single APB-coupled dislocation pairs and bowing-assisted cutting), but is computationally expensive. In this work, we present an approach that uses the numerical discrete dislocation (DD) model to build a fast spreadsheet model that may be of industrial use. A methodology to rapidly evaluate the yield strength of superalloys using a fast spreadsheet model was explored. The results from a physics-based discrete dislocation simulation model were fit to polynomials. These were used along with appropriate heuristic logic, to develop a spreadsheet that can predict the yield strength from the composition, and microstructural parameters of an alloy. The model was compared with data available for a series of superalloys and found to have good correspondence. 1.0 Introduction The nickel-based superalloys are a metallurgical marvel and have benefited from several decades of evolutionary changes. It is generally agreed by metallurgists that even in this class of the most evolved and complex alloys, the mechanical behavior is dictated almost entirely by the microstructure and chemistry of the phases. However it is also generally agreed that the ability to predict mechanical behavior poses great difficulties even when the microstructure and chemistry are well characterized in a given alloy. Of the various mechanical properties of design interest, the yield strength is likely the easiest to predict. There have been published works in which semi-empirical models were built using data from well-designed experiments with reasonable success. (see for example, Schirra 1 ) However for alloy design, and for studying effects of a wider range of variables, physics-based models are desired. The present work is an attempt at such a model. We begin with a brief description of the status of physicsbased models, to bring out the novelty of the present work. The paper is organized as follows. We start with a description of the microstructure as represented in the model, and a brief overview of the approach used to derive the spreadsheet model. We then present elements of this derivation, which include the numerical DD model. Next the results of a parametric study conducted using the physics-based numerical model is presented. The predicted dependence of the yield strength of superalloys on various microstrucutral parameters is shown. Finally the derivation of the spreadsheet model from these parametric studies is presented; the predictions of the spreadsheet model are shown compared with experimental data.