Evaluation of the method: Computational modeling of Jominy test with variable thermal properties using finite elements

Abstract

With the introduction of numerical methods, combined with powerful computational resources, a larger amount of problems of higher complexity could be solved compared to those solved by analytical methods. Analytical solutions, implied at the same time, huge efforts by means of complex mathematical formulation, and solution were restricted to a reduced number of physical problems. Research in numerical methods is being held all around the globe, and an important number of papers in many different areas are being published year after year. The main goal achieved by introducing numerical methods solutions is the possibility this methods gives, in order to obtain a closer-to-reality nonlinear solution, taking into account real geometry, non-independent material’s properties, initial and boundary conditions, and the evolution in time of geometry, material properties and boundary conditions. Jominy test (ASTM A255, SAE J406, ISO 642 / A04-303), is one of those physical test were an analytical solution could not be obtained due the dependence with temperature of material properties as density, specific heat capacity and thermal conduction. In this thesis, two different ways of modeling Jominy test by means of Finite Element Method are presented and compared. The first one is a series of MATLAB! codes, based on finite element theory, where Parabolic First Order Heat Conduction Equation is taken from its continuous time-space domain form, into the discrete time- space domain. In second place, modeling with CAM commercial software ANSYS! is being held, in order to obtain a solution with a proved, well known, CAM software, which allows having trustful results to compare with. Axisymmetric condition is taking into account to reduce the number of axis without losing any accuracy in both, MATLAB! and ANSYS! solutions. An Experimental framework chapter has been added in order to give a better understanding of Jominy test experiment for readers not related to it. It is, indeed, a general overview of the experiment. For a detailed explanation of the procedure it would be necessary for the reader to acquire the ASTM A255 standard of Jominy test, or any equivalent standard (SAE J406, ISO 642/ A04-303). The reader can find technical results from the test in [7], pages 323 and 324. If related with Jominy test, skip chapter one, Experimental Framework, as this introductory chapter is intended, as said before, to readers not related with the experiment in order to establish necessary background for a better understand of the work presented thereafter. Thesis is centered in the numerical results, the main objective is the to be able to conclude if the numerical algorithm implemented in MATLAB! represents indeed the real test, by means of comparing results with simulations made using a high level commercial proved CAM software ANSYS!. A complete and deep explanation of the Theoretical background related with the project is exposed in chapter 2 Theoretical Framework, including, among others, Thermal Parabolic first order equation reigning physical behavior of the specimen submitted to Jominy test, the finite element method applied to the heat-transfer equation, as well as finite difference method used later on in the time-domain. Special care was put into ensure compatibility between both results in order to make the analysis. Enhances have being done in order this comparison could take place and resemble most likely to the real test conditions: A variable mesh, closer to the real thermocouples position, was employed in both programs. In the variable mesh, implicit methods in time were implemented, and an easy to comprehend postprocessor was developed. Motivation for overtaking this thesis lies in observing the correlation in results obtained by own means, compared to those obtained by a trustful source, and this is the most important feature of the thesis. As expected, differences between two solutions are found, but same shape and similar gradient of temperature are obtained, proving the validity of previous results.