Ben-Gurion University of the Negev
Materials Engineering
Name of the module: Mechanical properties of materials 2
Number of module: 365-1-3121
BGU Credits: 4
Course Description
ECTS credits: 6
An advanced course on continuum aspects of the mechanical behavior of
Academic year: 2013- 2014
materials, repeating in more details the analysis of the elastic, plastic and fracture
Semester: Fall
behavior.
Hours of instruction: 3 lecture hours +
The displacement field, strain and stress are defined, their transformation
1exercise class hour per week
properties and principle values are found in 3D. The relation between
Location of instruction: room 203
displacements and strains (compatibility equation) is derived and the relation
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between stress and strain (constitutive equation like Hook's law) is defined.
Language of instruction: Hebrew
Combining these two equations with the second law of Newton and boundary
Cycle: First cycle
conditions allows to solve general problems in elasticity and illustrates the general
Position: a mandatory module for 3
rd
framework of continuum mechanics.
year undergraduate students in the
Two approaches to solve the equations of elasticity are studied: the Airy equation
Department of Materials Engineering
is derived and applied to solve several problems. Engineering applications of these
to be taken on Fall semester
solutions are illustrated. It illustrates analytic solution to simple problems (and is
Field
of
Education:
Materials
compare with the simple "strength of materials" approach). The mathematical
Engineering
background of the Finite Element Method is introduced. Several problems are
Responsible department: Materials
solved during classroom training with a commercial program. It illustrates numeric
Engineering
solutions to general problems.
General prerequisites: students should
The reasoning for the von Mishes and Tresca yield criterions is explained. Both
complete modules Mechanical
are applied to obtain analytic approximations to the stress distribution in plastic
properties 1
forming of metals and to determine the size of the plastic region at a crack tip. The
Grading scale: the grading scale
finite element approach is applied to obtain more accurate and detailed solution to
would be determined on a scale of 0 –
plastic and to contact problems, during class exercise.
100 (0 would indicate failure and 100
The third part of the course is devoted to fracture mechanics. Griffith and Irvin
complete success 0 to 100), passing
criteria for fast (unstable) crack propagation are derived and shown to be
grade is 56.
equivalent. The concepts of energy release rate, fracture resistance, stress intensity
factor and fracture toughness are studied. Experimental approaches to measure the
Lecturer: Prof. Roni Shneck
fracture toughness are described, and compared to uniaxial tension test. Relations
Contact details: room 9, building 59
between microstructure and fracture toughness are reinvestigated.
Office phone: 08-6472493
The linear fracture mechanics is extended to plastic materials by the R curve and J
Email: roni@bgu.ac.il
integral approaches. Threshold stress intensity factor, small fatigue cracks and
Office hours: Tuesday, from 11 to
limitation of fracture mechanics. The distinction between S-N curve and fatigue
13AM.
crack propagation rate experiments It is extended to stable crack propagation, in
particular to fatigue crack propagation. Fracture mechanics leads to the realization
Module evaluation: at the end of the
that any engineering component contains defects that may propagate. Applications
semester the students will evaluate the
of the knowledge of mechanical behavior and fracture mechanics are found in the
module, in order to draw conclusions,
four categories of modern engineering design for fatigue and fracture prevention:
and for the university's internal needs.
safe life, proof testing, fail safe and damage tolerance.
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Ben-Gurion University of the Negev
Materials Engineering
Confirmation:
the
syllabus
was
Aims
Develop firm understanding of the notions of continuum mechanics, stress
confirmed by the faculty academic
advisory committee to be valid on
distribution in solids and the roles that govern it. Develop the capability of stress
2013-2014.
analysis in the elastic regime, in five levels: intuitive level, simple 'strength of
Last update:
material' approach, exact analytic approach and numeric calculations.
Understand the conditions of stress required to induce plastic deformation.
Application for metal forming and for fracture.
Familiarity with fracture mechanics of brittle and ductile materials. Applications
of the theory to fatigue, its successful results and limitations. Application in modern
engineering design approaches
.
Objectives of the module
The objectives of the course are to learn, understand and earn the ability to apply in
engineering design and materials selection the mechanical behavior of metals and
ceramics. These aims include elementary stress analysis and calculations,
familiarity with dislocation behavior and strengthening mechanisms of metals,
criterion for fast crack propagationin brittle and ductile materials, the phenomenon
of fatigue and its prevention.
Attendance regulation: attendance and participation in class is mandatory.
Teaching arrangement and method of instruction: The module consists of lectures
and exercises.
Assessment:
1.
Exam
35- 85%
2.
Quiz
10% (not mandatory)
3.
Homework 15%
4.
Finite Element project 20-40%
100%
Work and assignments: Student will conduct 6 home works related to the exercises
in the class.
Quiz: midterm, open questions.
Exam: at the end of semester, open questions.
Time required for individual work: in addition to attendance in class, the students
are expected to do their assignment and individual work: at least two hours per
week, 10 hours before the quiz and 24 hours before exam.
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Ben-Gurion University of the Negev
Module Content / schedule and outlines
Materials Engineering
(a) Elasticity
Definition of strain (the continuity equation), stresses and their transformation laws (reading duty), principle strains and
stress in 3D, invariants of the stress and strain tensors.
Hook's law in general anisotropic 3D material.
The equations of equilibrium.
The Airy function approach to simultaneously solve the three equations of elasticity a home duty.
Applications of Airy function approach to illustrate exact analytic solutions of a few problems: bending of beams, a
cylinder with internal pressure and stress concentration around a circular hole. The engineering applications of these
solutions are illustrated in home exercise.
Introduction to the mathematical background of the finite element method (FEM).
Training the use of a commercial program to solve foure example problems. Apply symmetry, local refining and
distribution of the external loads in order to save computer resources and decrease computation errors.
Individual projects in FEM analysis (elective home duty).
(b) Plasticity
The derivation and graphical illustration of von Mishes and Tresca criteria for yielding in 3D materials, based on
experimental observations and the invariants of the stress tensor.
Applications of the yield criteria to solve problems in metal forming.
A Finite Element example of a problem in plasticity
(c) Fracture Mechanics
Griffith and Irvin criteria for fast crack propagation are compared.
The concepts of energy release rate, fracture resistance, stress intensity factor and fracture toughness are reviewed.
Experimental approaches to determine the fracture toughness.
Relations between microstructure and fracture toughness.
Extension of the linear theory to plastically deforming materials by the R curve and J integral approaches.
Extension of fracture mechanics to fatigue crack propagation. Fatigue crack propagation rate as function of the
amplitude of stress intensity factor. Paris law. Application to fatigue life prediction.
Applications of fracture mechanics in the four categories of modern engineering design for fatigue and fracture
prevention: safe life, proof testing, fail safe and damage tolerance.
The creep of metals is learnt as a home duty.
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Ben-Gurion University of the Negev
Materials Engineering
Exercises:
3D transformation of stress and strain
Solution of 2D problems in elasticity with Airy functions and engineering applications.
Four classroom exercises in Finite Element modeling of elastic and contact problems.
Analytic application of Von Mishes and Tresca criteria for plastic forming of metals
Finite Element modeling of plastic forming.
Linear elastic fracture mechanics: finding stress intensity factors, residual strength, unstable crack propagation
Applications for fatigue, rate of propagation of fatigue cracks, fatigue life prediction
Required reading:
1. V. E. Saouma, Introduction to Mechanics of Materials, 2002.
2. E. Dieter, Mechanical Metallurgy, McGraw Hill, 1988 (TA405 D53 1988).
2.
R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, Wiley, 1996.
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