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 closertoreality nonlinear
solution, taking into account real geometry, nonindependent
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 / A04303), 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 timespace 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/ A04303). 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 heattransfer equation, as well as finite
difference method used later on in the timedomain.
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. 