Simple models for the omega phase transformation

In the late sixties, it was recognized that the omega phase transformation occurring in bcc Ti, Zr, and Hf alloys was a displacive transition which could be described, at least qualitatively, by simple models. Since the displacive wave responsible for the transition to perfect omega was a Brillouin zone boundary wave, displacements and volume changes were rather small, in contrast to the classical martensite case. The nonideal, or modulated omega phase requires further consideration, and calls for soliton models, for example. Recent first principles electronic structure calculations, briefly reported upon here, have also shed light on the athermal omega transformation. This paper is based on a presentation made in the symposium “Pre-transformation Behavior Related to Displacive Transformations in Alloys≓ presented at the 1986 annual AIME meeting in New Orleans, March 2-6, 1986, under the auspices of the ASM-MSD Structures Committee.     

Application of the method of reference points for calculating the density of strips rolled from powders

Summary An analysis of experimental data on the relationship between the density and thickness of strips rolled from iron, nickel, aluminum, titanium, and stainlesssteel powders in rolling mills with different roller diameters was performed. It was shown that the dependence of the density on the thickness of strips is determined by the method used for varying the strip thickness.It was found that the density of strips heavily depends on the strip width. A method for calculating the density of rolled strips which takes into account all the geometric and physicomechanical parameters of the process and which yields results that are in good agreement with experimental data was proposed.     

Numerical models for casting solidification: Part II. Application of the boundary element method to solidification problems

A new numerical model, which is based on the boundary element method, was proposed for the simulation of solidification problems, and its application was demonstrated for solidification of metals in metal and sand molds. Comparisons were made between results from this model and those from the explicit finite difference method. Temperature recovery method was successfully adopted to estimate the liberation of latent heat of freezing in the boundary element method. A coupling method was proposed for problems in which the boundary condition of the interface consisting of inhomogeneous bodies is governed by Newton’s law of cooling in the boundary element method. It was concluded that the boundary element method which has several advantages, such as the wide variety of element shapes, simplicity of data preparation, and small CPU times, will find wide application as an alternative for finite difference or finite element methods, in the fields of solidification problems, especially for complex, three-dimensional geometries. On leave from Kyung-Pook National University, Taegu, Korea     

Regression models: calculating the confidence interval of effects in the presence of interactions

The main goal of regression analysis (multiple, logistic, Cox) is to assess the relationship of one or more exposure variables to a response variable, in the presence of confounding and interaction. The confidence interval for the regression coefficient of the exposure variable, obtained through the use of a computer statistical package, quantify these relationships for models without interaction. Relationships between variables that present interactions are represented by two or more terms, and the corresponding confidence intervals can be calculated 'manually' from the covariance matrix. This paper suggests an easy procedure for obtaining confidence intervals from any statistical package. This procedure is applicable for modifying variables which are continuous as well as categorical.