2020 Fundamentals of Stress and Strain, and Deformation of Metals

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Takeyama Masao  Onaka Susumu 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue1-2(S621)  Fri1-2(S621)  
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Offered quarter
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Course description and aims

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.

Student learning outcomes

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.


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 that will be developed

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/Required learning

  Course schedule Required learning
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 Plastic deformation (yielding phenomena) Understanding of yielding and motion of dislocations
Class 9 Ideal strength and crystal defects Differences in strength of crystals with and without dislocations
Class 10 Crystal plasticity and glide motion of dislocation Understanding of slip motion of dislocations
Class 11 Plastic deformation of single crystal (geometry of slip deformation) Understanding of Shmid's law and critical resolved shear stress
Class 12 Plastic deformation of polycrystal (role of grain boundary) Understanding of Hall-Petch relationship
Class 13 Deformation mechanisms and strengthening methods Work hardening,solid-solution strengthening, precipitate strengthening, dispersion strengthening
Class 14 Exercise problems for the second half of this course Students will be assessed on their understanding of plastic deformation, crystal defects and strengthening methods of metals and alloys, and their ability to apply them to solve problems

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.


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

Assessment criteria and methods

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%.

Related courses

  • MAT.M303 : Lattice Defects and Dislocation

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

None required.



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