Section 6.5
True Stress and True Strain
1
The engineering stress-strain behavior for the brass specimen (Cu-Zn).
2
-Metals seems to soften beyond T.S (point A) due to definition of
engineering stress-strains relative to original dimensions.
l
=
l0
=
P
A0
A colleague was once telling me how his students were struggling with log laws. He said his
students seemed to suffer from what he referred to as the "log law blahs". Another colleague
overheard our conversation, interrupted us and said he had heard and r
Monday, April 8 Lecture 36 : Lengths of polar curves and areas of polar regions.
(Refers to Section 9.3, 9.4)
After having practiced the problems associated to the concepts of this lecture the student should
be able to : Find the length of a polar curve w
Friday, April 5 Lecture 35 : Graphing polar equations - Tangents to polar curves
(Refers to Section 9.3)
After having practiced the problems associated to the concepts of this lecture the student should be able to :
Graph a polar equation r = f( ) by usin
Wednesday, April 3
Section 9.3)
Lecture 34 : Polar Coordinates and polar equations (Refers to
After having practiced the problems associated to the concepts of this lecture the student should
be able to : Express polar coordinates in Cartesian coordinates
Monday, April 1 Lecture 33 : Parametric Equations, curves and tangents (Refers
to Section 9.1, 9.2)
After having practiced the problems associated to the concepts of this lecture the student
should be able to : Plot simple parametric equations in the plan
Wednesday, March 27 Lecture 32 : Applications : Evaluation of definite integrals and
limits. (Refers to Section 8.9 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
Use a Taylor se
Monday, March 25 Lecture 31 : Applications : Approximating the value of a series or a
function. (Refers to Section 8.9 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to: Use a
Taylor
Friday, March 22 Lecture 30 : Examples on determining the function which
generates a series. (Refers to Section 8.8 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be
able to: Find the functi
Wednesday, March 20
text)
Lecture 29 : Binomial series (Refers to Section 8.8 in your
After having practiced the problems associated to the concepts of this lecture the student should be able to:
State and apply the Binomial series theorem.
29.1 Introduct
Monday, March 18 Lecture 28 : Taylor's remainder theorem: Convergence of a
series to its generator (Refers to Section 8.8 in your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
Define th
Friday, March 15 Lecture 27 : Taylor series and Maclaurin series generated by a
function f(x). (Refers to Section 8.8 your text)
After having practiced the problems associated to the concepts of this lecture the student should be able to:
Define a Taylor
Math 118
Problem Solving Methods
Overview:
This guide is intended as a supplement to the course. The assumption is made that the student has already seen much of the
material presented here, and has a solid grasp of the basics of limits, integrals and der
ME115
Structure & Properties of Materials
Winter 2013
1
Chapter 1:
Introduction to Materials Science &
Engineering
2
3
Application of the tetrahedron of materials science and engineering, Askeland, et al.
Types of materials,
Askeland.
4
Selecting and Desi
Section 6.4
Properties Obtained from the Tensile Test,
Conted
1
Example
An aluminum rod is to withstand an applied force of 45,000 pounds.
To assure a sufficient safety, the maximum allowable stress on the
rod is limited to 25,000 psi.
The rod must be at
Chapter 6
Mechanical Properties: Part I
1
Objectives of Chapter 6
Introduce the basic concepts associated with mechanical
properties of materials.
Evaluate factors that affect the mechanical properties of
materials.
Review some of the basic testing pro
Section 4.5
Schmids Law, Conted
1
Example
A single crystal of an FCC metal is oriented so that the [001]
direction is parallel to an applied stress of 5000psi.
Calculate the resolved shear stress acting on the (111) slip
[ 1 1 0]
plane in the
slip directi
Section 4.5
Schmids Law
1
Plastic deformation - Permanent deformation caused by
dislocations moving through the metal. Anything that
impedes dislocation mobility strengthens the metal at the
expense of ductility.
Elastic deformation Reversible deformati
Section 4.3
Dislocations
1
Thought experiment:
If we bend a metal bar, and there are no cracks on the outer radius
or wrinkles on the inner radius, is the length on inner and outer
surface still the same?
Why or why not?
2
Atomic Movements During Permanen
Chapter 4
Imperfections in the Atomic and Ionic
Arrangements
1
Objectives of Chapter 4
Introduce the three basic types of imperfections:
1. Point defects,
2. Line defects (or dislocations), and
3. Surface defects.
Explore the nature and effects of diffe
Section 3.6
Interstitial Sites
1
Interstitial sites - Locations between the
normal atoms or ions in a crystal into which
another - usually different - atom or ion is
placed. Typically, the size of this interstitial
location is smaller than the atom or io
Section 3.5
Points, Directions, Planes and the Unit Cell
1
Miller indices - A shorthand notation to describe certain
crystallographic directions and planes in a material.
Denoted by [ ] brackets. A negative number is represented
by a bar over the number.
Section 3.3
Continued
Lattice, Unit Cells, Basis, and Crystal
Structures
1
the Relationships Between the Atomic Radius and
the Lattice Parameter in Cubic Systems
SC
a 0 = 2r
BCC
4r
a0 =
3
FCC
4r
a0 =
2
2
Packing Factor or Atomic Packing Fraction (APF)
Fr
Chapter 3:
Atomic and Ionic Arrangements
1
Section 3.1
Short-Range Order
versus
Long-Range Order
2
Levels of Atomic Arrangements in Materials
a. Inert monoatomic
gases have no regular
ordering of atoms.
b & c. Water vapor, nitrogen
gas, amorphous silicon
Chapter 2:
Atomic Structure Continued
1
Ionic Bonding
Askeland
Occurs when more than one type of atom is present in a
material, one atom may donate its valence electrons to a different
atom, filling the outer energy shell of the second atom.
The opposit
Wednesday, March 13 Lecture 26 : Expressing functions as a power series:
Derivatives and Integrals of power series. (Refers to Sections 8.6 and 8.7 )
After having practiced the problems associated to the concepts of this lecture the student should be
able
Monday, March 11 Lecture 25 : Expressing a power series as a function and
operations on power series. (Refers to Section 8.7 )
After having practiced the problems associated to the concepts of this lecture the student should be
able to: Determine the sum,
Friday, March 8 Lecture 24 : Power Series and their interval of convergence.
(Refers to Section 8.6 in your text)
After having practiced the problems associated to the concepts of this lecture the student
should be able to: Define a power series centered
Wednesday, January 23 Lecture 9 : Error estimation for numerical integration.
(Refers to section 5.3)
After having practiced the problems associated to the concepts of this lecture the student should
be able to: Find error's bounds when applying either th