Numerical Methods
(Chapters 19 and 20, Kreyszigs Book 9th Ed.)
Numerical methods for solving nonlinear
equation by iteration
Numerical solution of linear systems
Interpolation and inverse interpolation
Numerical Integration and Differentiation
1
Introd
Linear Algebra
(Chapter 7, Kreyszigs Book)
Concepts and operations of matrices
Systems of linear algebraic equations
Rank of a matrix
Determinant of a matrix
Inverse of a matrix
Eigenvalue and eigenvector
Least squares method
1
Matrix
A matrix is a
Probability
(Chapters 24, Kreyszigs 9th Ed.
Chapter 2 Navidis 1st or 2nd Ed.)
Introduction to probability
Counting methods
Conditional probability and independence
with engineering applications
Random variables
1
Introduction to Probability
The develo
Hypothesis Test
(Chapters 25.4, Kreyszigs 9th Ed.
Chapter 6 Navidis 1st or 2nd Ed.)
Hypothesis test for a population mean
using normal distributions
Hypothesis test for a population mean
using student tdistribution
Hypothesis test for the difference be
Sampling and distribution
(Chapters 24,25, Kreyszigs 9th Ed.
Chapter 1 and 4 Navidis 1st or 2nd Ed.)
Sampling and data representation
Common probability distributions
Parameter estimation and simple statistical
inference
1
Data and statistical inference
Confidence Interval
(Chapters 25.3, Kreyszigs 9th Ed.
Chapter 5 Navidis 1st or 2nd Ed.)
Confidence interval for a population mean
using normal distributions
Confidence interval for a population mean
using student tdistribution
Confidence interval for t
ME251.3 Engineering Analysis I
Department of Mechanical Engineering
University of Saskatchewan
Prof. FangXiang WU, Ph.D.
Email: [email protected]
Telephone: (306)9665280
Office: ENG 3B42
1
Lectures and Tutorial
Lecture Time: MWF, 10:30am11:20 am
L
Midterm Review
ME251: Engineering Analysis
Department of Mechanical Engineering
University of Saskatchewan
Professor FangXiang Wu
Probability
(Chapters 24, Kreyszigs 9th Ed.
Chapter 2 Navidis 1st or 2nd Ed.)
Introduction to probability
Counting methods
Co
Example for final reviews
April 2015
1. (2009)There are 8 main traffic intersections in Saskatoon downtown. Averagely two traffic
accidents per week occur at each of these intersections. A) What is the probability that more than
one traffic accident occur
Final Review
ME251: Engineering Analysis
Department of Mechanical Engineering
University of Saskatchewan
Professor FangXiang Wu
Probability
(Chapters 24, Kreyszigs 9th Ed.
Chapter 2 Navidis 1st or 2nd Ed.)
Introduction to probability
Counting methods
Cond
Extra examples for Midterm
review
ME251
Department of Mechanical Engineering
University of Saskatchewan
Professor FangXiang Wu
Example 1
A certain plant runs three shifts per day. Of all the
items produced by the plant, 50% of them are
produced on the fi
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
Comparison of XRays, Neutron and
Electron Scattering
Xray
Xray are scattered primarily by the atomic
electrons
Difficult for Xray to detect the light atoms
and to distinguish between elements of
similar atomic number
High absorption coefficient
Com
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
ORIENTATION IMAGING
MICROSCOPY
2
OIM as a New Tool
Xray Diffraction
Optical M. & SEM
 Pole Figures & ODF
with image
analysis
 Phase Analysis
Orientation Imaging
Microscopy
TEM
F. Friedel, et al. (1999)
What is the OIM ?
A technique enables a visual rep
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
Using Neutrons
Neutrons have to be extracted from the
nuclei of atoms. Methods used:
Fission process: 235U nuclei breakes into
two lighter fragments and 23 neutrons.
Spallation process: high energy proton
bombardment of lead, release of neutrons
Fission
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
Diffracted Intensity
1.
2.
3.
4.
5.
6.
Polarization factor
Structure factor
Multiplicity factor
Lorentz factor
Absorption factor
Temperature factor
X ray scattering: Scattering by an electron
Electric field strength varies with time at anyone point in
the
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
Counting XRays
Proportional counter
Scintillation counter
Semiconductor
CCD detectors
Proportional counter
Gas counter (proportional or
Geiger) and basic circuit
connections
Effect of voltage on the gas
amplification factor
Proportional counter
Ionizatio
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
Introduction
What is a Synchrotron XRadiation?
Electromagnetic radiation that is emitted by
charged particles moving at relativistic
speeds (velocity of light) in circular orbits in a
magnetic field.
1/19
Introduction
Schematic view of a synchrotron li
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
GENERATION OF XRAYS
Generation of XRays
1895
1912
Roentgen
Von Laue, W. L. Bragg
Rotating Anodes
Xray spectrum of molybdenum as a function of applied
XRay Radiation
The Wave
x
E A sin 2 t
A : amplitude of the wave
: wavelength
: frequency
XRay Pho
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
The Structure and Energy
of Interfaces
The Structure and Energy of Grain
Boundaries
Our ability to understand the phenomena of
recovery, recrystallization and grain growth depends
on our knowledge of the grain boundaries.
High angle grain boundaries (HAG
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
INTRODUCTION TO
TEXTURE
What is Texture ?
For many people, texture characterizes structure of
Textile
Wood
Geological fibers
Geological deposits
For materials researchers, the texture has another
meaning
Texture is used to characterizes the orientation
Structure and Properties of Polycrystalline Materials
ME 498

Spring 2016
WHAT WE PLAN TO DO
OBJECTIVES
To learn methods of quantitative description of structure of
polycrystalline engineering materials.
To learn experimental techniques of texture measurements interfaces
characterization.
To develop understanding of the thermo
IMPERFECTIONS IN SOLIDS
EXAMPLE PROBLEMS
Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327C (600 K).
Assume an energy for vacancy formation of 0.55 eV/atom.
Solution
In order to compute the fraction of atom si
Topic 8: Introduction to
Manufacturing
ISSUES TO ADDRESS.
How do we fabricate metals?
How do we fabricate ceramics?
How do make polymers?
How do We Make Things?
(Manufacturing)
We can think of several general methods:
Build a hole and fill it with the
Topic 7: Phase Diagrams
Learning Objectives
Understand the basic concepts related to phase
diagrams
Given a binary phase diagram, the composition and
the temperature, be able to determine
 the phase (s) is (are) present,
 the composition (s) of the ph
Topic 6: Diffusion in Solids
ISSUES TO ADDRESS.
How does diffusion occur?
Why is it an important part of processing?
How can the rate of diffusion be predicted for
some simple cases?
How does diffusion depend on structure
and temperature?
Activated Ra
UNIVERSITY OF SASKATCHEWAN
COLLEGE OF ENGINEERING
MECHANICAL ENGINEERING (M.E.) 214
ALL SECTIONS
MIDTERM EXAM
Question 1 (27 marks)
a
List the four important components involved in materials science and engineering and describe
their relationship (4 mark
Topic 3: The Structure of
Crystalline Solids
ISSUES TO ADDRESS.
How do atoms assemble into solid materials?
(for now, focus on metals)
How does the density of a material depend on
its structure?
When do material properties vary with the
sample (i.e., p
Introduction (Chapter 1)
What are engineering materials?
Why should engineers study materials? What should they
know about them?
The life cycle of the materials
Structure, processing, properties and performance of
materials
Materials science and engi