2024 Faculty Courses School of Materials and Chemical Technology Department of Materials Science and Engineering Graduate major in Materials Science and Engineering
Kinematical theory of microstructure formed by diffusionless phase transformation
- Academic unit or major
- Graduate major in Materials Science and Engineering
- Instructor(s)
- Tomonari Inamura / Masaki Tahara
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon / 3-4 Thu
- Class
- -
- Course Code
- MAT.M431
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
Microstructures of low symmetry phase formed by diffusionless transformations in shape memory alloys, steels, piezoelectrics often exhibit characteristic patterns. This lecture give a kinematic theory of the microstructure formed by such diffusionless transformations. The basis of the theory is nonlinear solid mechanics. First, we will outline the necessary basic mathematics and learn the kinematic compatibility condition that is the key to the theory. Second, we apply the theory to some transformations to understand how to use the theory. The purpose of this lecture is to learn the theoretical basis of the microstructure of diffusionless transformation and how to analyze the microscopy data.
Course description and aims
Learn the method to compute the geometrical and crystallographic quantities that characterize the microstructures of diffusionless transformation using kinematic compatibility conditions, and use it to analyze experimental data and design of materials.
Keywords
Martensite, Shape memory alloy, Steel, Ferroic material, Kink deformation, Geometrically nonlinear theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lectures will include mathematics and material science which is necessary to understand the theory. The important theorems and propositions are described up to the proof method. A few quizzes will be given in the lectures to deepen your understanding.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction | Review what is martensite. Purpose of this lecture is shown. |
| Class 2 | Vector, matrix and coordinate transformation | Basics of vector, matrix and coordinate transformation |
| Class 3 | Eigenvalue problem | Review the eigenvalues, eigenvectors and diagonalization of matrix |
| Class 4 | Polar decomposition theorem | Decomposition of regular matrix into the product of orthogonal matrix and symmetric matrix. |
| Class 5 | Deformation in 3D:I | Reference and deformed configurations, deformation and displacement gradients are defined |
| Class 6 | Deformation in 3D: II | Deformation of line element, area element and volume element, strain tensors |
| Class 7 | Kinematic compatibility | Kinematic compatibility conditions based on the continuity of deformation at interface |
| Class 8 | Crystallography of martensite | Braves lattice, lattice correspondence, lattice deformation, variant |
| Class 9 | Twin and twining equationn | Crystallographic definition of twin, twining equation |
| Class 10 | Parent-martensite interface | Kinematic compatibility at habit plane of martensite |
| Class 11 | Self-accommodation microstructure | The condition for the compatible phase transformation microstructure |
| Class 12 | Comparison with classical theory of martensite crystallography | Comparison with the phenomenological theory of martensite crystallography |
| Class 13 | Examples : Martensite microstructures | Analysis of martensite microstructures in shape memory alloys and steels. |
| Class 14 | Examples: Application to deformation microstructures | Application to the kink deformation |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
K. Bhattacharya, "Microstructure of martensite", Oxford University Press
Reference books, course materials, etc.
Lecture materials will be distributed every lecture
Evaluation methods and criteria
Grades will be evaluated based on quizzes (50%) and reports (50%).
Related courses
- MAT.M201 ： Fundamentals of Crystallography
- MAT.M401 ： Applied Diffraction Crystallography in Metals and Alloys
- MAT.M410 ： Deformation and Strength of Solids
- LAS.M102 ： Linear Algebra I / Recitation
Prerequisites
This lecture is intended for those who have learned the basics of linear algebra, crystallography, and phase transformation in the undergraduate program. It is recommended to obtain software that can perform numerical calculations using matrices.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
inamura.t.aa[at]m.titech.ac.jp