2024 Faculty Courses School of Materials and Chemical Technology Undergraduate major in Materials Science and Engineering

Fundamentals of Stress and Strain, and Deformation of Metals

Academic unit or major: Undergraduate major in Materials Science and Engineering
Instructor(s): Yoshihiro Terada / Susumu Onaka
Class Format: Lecture (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 1-2 Tue / 1-2 Fri
Class: -
Course Code: MAT.M205
Number of credits: 200
Course offered: 2024
Offered quarter: 4Q
Syllabus updated: Mar 17, 2025
Language: Japanese

Syllabus

Course overview and goals

To consider deformation and strength of metals and alloys, understanding stresses and strains as tensors is needed. The first half of this course teaches the fundamentals of stresses and strains and the relationship between stresses and strains during elastic deformation known as Hooke's law. On the other hand, the second half teaches the plastic deformation of metals and alloys from both microscopic and macroscopic points of view, and explains various strengthening methods on the basis of plastic deformation of crystals and roles of dislocations.

Course description and aims

By completing this course, students will be able to:
1) Understand the fundamentals of stresses and strains that are second-rank tensors.
2) Understand the plastic deformation of engineering materials, the atomistic mechanisms of plastic deformation and the roles of dislocations.

Keywords

stress, strain, tensor, transformation of coordinate systems, distortion, elastic deformation, plastic deformation, Hooke's law, Young's modulus, Poisson's ratio, bulk modulus, shear modulus, elastic coefficients, dislocation, slip deformation, Schmid's law, critical resolved shear stress, yield stress, proof stress, tensile strength, fracture strain, work hardening, strengthening mechanisms, solid-solution strengthening, precipitate strengthening, dispersion strengthening, grain boundary, Hall-Petch relationship.

Competencies

Specialist skills
Intercultural skills
Communication skills
Critical thinking skills
Practical and/or problem-solving skills

Class flow

Exercise problems are assigned during the course. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	The concept of stress and strain, and deformation of metals and alloys	Deformation and fracture of metals and alloys, Characteristic variables of stress-strain curve such as Young's modulus, yield stress and tensile strength
Class 2	Most simplified expression of stress and strain	Tensile deformation of cylindrical specimen, Load-elongation curve and stress-strain curve
Class 3	Definition of traction (vector) and stress (tensor)	Understanding of traction and stress
Class 4	Relationships satisfied for stress components	Symmetry of stress components, Relationship between traction and stress. Summation convention of indexed variables
Class 5	Definition of distortion and strain	Understanding of the concept of distortion and straintensor components
Class 6	Elastic coefficients and Hooke's law	Elastic coefficients as tensors, Elastic deformation of elastically isotropic materials
Class 7	Exercise problems for the first half of this course	Students will be assessed on their understanding of stress and strain, and their ability to apply them to solve problems
Class 8	Evaluation of metal strength	Tensile test and creep test, low-temperature strength and high-temperature strength
Class 9	Plastic deformation and lattice defect	Defects in metal crystal, dislocation glide and dislocation climb, deformation of metals in macroscopic scale and dislocation motion in microscopic scale, Orowan's equation
Class 10	Peierls stress	Ideal strength, dislocation slip in crystal, interplanar spacing, interatomic distance
Class 11	Slip system 1	Edge dislocation and screw dislocation, Burgers vector and dislocation line vector, the plane with the greatest planar density and the direction with the highest linear density in crystal
Class 12	Slip system 2	Utilization of standard stereographic projection, great circle, standard stereographic triangle
Class 13	Yielding of single crystal	Polycrystal and single crystal, Schmid factor, Schmid's law and critical resolved shear stress
Class 14	Exercise problems for the second half of this course	Students will be assessed on their understanding of evaluation of metal strength, plastic deformation and lattice defect, Peierls stress, slip system, and yielding of single crystal

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)

None required.

Reference books, course materials, etc.

W. D. Callister, Jr: Materials Science and Engineering An Introduction, John Wiley and Sons, Inc.
S. Kohda: Plasticity of metals, Maruzen.
A. Kelly and G. W. Groves: Crystallography and Crystal Defects, Longman Group Ltd., London

Evaluation methods and criteria

Students' knowledge of stress and strain, deformation of single crystal and polycrystal, and their ability to apply them to problems will be assessed. Midterm and final exams 80%, exercise problems 20%.