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2023　Kinematical theory of microstructure formed by diffusionless phase transformation

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Academic unit or major
Graduate major in Materials Science and Engineering
Instructor(s)
Inamura Tomonari  Tahara Masaki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(G1-103 (G114))  Thr3-4(G1-103 (G114))  
Group
-
Course number
MAT.M431
Credits
2
Academic year
2023
Offered quarter
1Q
Syllabus updated
2023/4/13
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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

Out-of-Class Study Time (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

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

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

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