Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Chapter Outline: Polymer Structures
Hydrocarbon and polymer molecules
Chemistry of polymer molecules
Molecular weight and shape
Molecular structure and configurations
Thermoplastic and thermosetting polymers
Copolymers
Polymer crystals and degree of cryst
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Fatigue
(Failure under fluctuating / cyclic stresses)
Under fluctuating / cyclic stresses, failure can occur at
loads considerably lower than tensile or yield strengths of
material under a static load: Fatigue
Estimated to causes 90% of all failures of me
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Fatigue: SN curves (III)
In most alloys, S decreases continuously with N. In this
cases the fatigue properties are described by
Fatigue strength: stress at which fracture occurs after a
specified number of cycles (e.g. 107)
Fatigue life: Number of cycles
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Creep
Creep is a timedependent and permanent deformation
of materials when subjected to a constant load at a high
temperature (> 0.4 Tm). Examples: turbine blades, steam
generators.
Creep testing:
Furnace
MSE 2090: Introduction to Materials Science
Chapt
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Mechanisms of Creep
Different mechanisms are responsible for creep in different
materials and under different loading and temperature
conditions. The mechanisms include
Stressassisted vacancy diffusion
Grain boundary diffusion
Grain boundary sliding
Disl
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Chapter Outline: Phase Diagrams
Microstructure and Phase Transformations in
Multicomponent Systems
Definitions and basic concepts
Phases and microstructure
Binary isomorphous systems (complete solid solubility)
Binary eutectic systems (limited solid solub
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Phase diagram
Phase diagram is a graphical representation of all the
equilibrium phases as a function of temperature, pressure,
and composition.
For one component systems, the equilibrium state of the
system is defined by two independent parameters (P and
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Binary Isomorphous Systems (I)
Isomorphous system  complete solid solubility of the two
components (both in the liquid and solid phases).
L
+L
Three phase region can be identified on the phase diagram:
Liquid (L) , solid + liquid ( +L), solid ( )
Liquidu
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
NonsteadyState Diffusion: Ficks second law
C
C
=D
t
x 2
2
Ficks second law relates the rate of change of composition
with time to the curvature of the concentration profile:
C
C
x
C
x
x
Concentration increases with time in those parts of the
system where
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Derivation of the lever rule
1) All material must be in one phase or the other:
W + WL = 1
2) Mass of a component that is present in both phases
equal to the mass of the component in one phase +
mass of the component in the second phase:
WC + WLCL = Co
3)
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Development of microstructure in isomorphous alloys
Fast (nonequilibrium) cooling
Compositional changes require diffusion in solid and
liquid phases
Diffusion in the solid state is very slow. The new
layers that solidify on top of the existing grains h
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Binary Eutectic Systems (V)
Compositions and relative amounts of phases are
determined from the same tie lines and lever rule, as for
isomorphous alloys
A
B
C
For points A, B, and C calculate the compositions (wt. %)
and relative amounts (mass fractions)
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Development of microstructure in eutectic alloys (V)
Compositions other than eutectic but within the range of
the eutectic isotherm
Primary phase is formed in the + L region, and the
eutectic structure that includes layers of and phases
(called eutectic a
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Phase diagrams with intermetallic compounds
Besides solid solutions, intermetallic compounds, that
have precise chemical compositions can exist in some
systems.
When using the lever rules, intermetallic compounds are
treated like any other phase, except t
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
The IronIron Carbide (FeFe3C) Phase Diagram
In their simplest form, steels are alloys of Iron (Fe) and
Carbon (C). The FeC phase diagram is a fairly complex
one, but we will only consider the steel part of the diagram,
up to around 7% Carbon.
MSE 2090: I
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Development of Microstructure in Iron  Carbon alloys
Microstructure depends on composition (carbon
content) and heat treatment. In the discussion below we
consider slow cooling in which equilibrium is maintained.
Microstructure of eutectoid steel (I)
MSE
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Crack propagation
Cracks with sharp tips propagate easier than cracks having
blunt tips
1/ 2
m
a
2 0
t
In ductile materials, plastic deformation at a crack tip
blunts the crack.
deformed
region
brittle
ductile
Energy balance on the crack
Elastic strain
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Ductile Fracture
(Cupandcone fracture in Al)
tensile failure
shear failure
Scanning Electron Microscopy: Fractographic studies at
high resolution. Spherical dimples correspond to
microvoids that initiate crack formation.
MSE 2090: Introduction to Materi
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Chapter Outline: Failure
How do Materials Break?
Ductile vs. brittle fracture
Principles of fracture mechanics
Stress concentration
Impact fracture testing
Fatigue (cyclic stresses)
Cyclic stresses, the SN curve
Crack initiation and propagation
Factors th
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Diffusion Temperature Dependence (II)
b = logD0
a=
y = ax + b
Qd
2.3R
x = 1/T
Graph of log D vs. 1/T has slop of Qd/2.3R,
intercept of log Do
Qd 1
log D = log D0
2.3R T
log D1 log D 2
Qd = 2.3R
1 T1 1 T2
MSE 2090: Introduction to Materials Science
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Diffusion: Role of the microstructure (I)
Selfdiffusion coefficients for Ag depend on the diffusion
path. In general the diffusivity if greater through less
restrictive structural regions grain boundaries, dislocation
cores, external surfaces.
MSE 2090:
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
StressStrain Behavior
Elastic Plastic
Elastic deformation
Reversible: when the stress
is removed, the material
returns to the dimensions it
had before the loading.
Stress
Usually strains are small
(except for the case of some
plastics, e.g. rubber).
Plas
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Elastic Deformation: Poissons ratio
Unloaded
Loaded
y
x
= =
z
z
Materials subject to tension shrink laterally. Those
subject to compression, bulge. The ratio of lateral and
axial strains is called the Poisson's ratio . Sign in
the above equations shows th
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Tensile Strength
If stress = tensile strength is maintained
then specimen will eventually break
Stress,
fracture
strength
Necking
Tensile strength: maximum
stress (~ 100  1000 MPa)
Strain,
For structural applications, the yield stress is usually a
more
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Elastic Recovery During Plastic Deformation
If a material is deformed plastically and the stress is then
released, the material ends up with a permanent strain.
If the stress is reapplied, the material again responds
elastically at the beginning up to a n
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Chapter Outline
Dislocations and Strengthening Mechanisms
What is happening in material during plastic deformation?
Dislocations and Plastic Deformation
Motion of dislocations in response to stress
Slip Systems
Plastic deformation in
single crystals
polyc
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Interactions between dislocations
The strain fields around dislocations cause them to
interact (exert force on each other). When they are in
the same plane, they repel if they have the same sign
(direction of the Burgers vector) and attract/annihilate
if
Introduction to the Science and Engineering of Materials
MSE 2090

Fall 2010
Slip in single crystals  critical resolved shear stress
When the resolved shear stress becomes sufficiently large,
the crystal will start to yield (dislocations start to move
along the most favorably oriented slip system). The onset
of yielding correspon