Fatigue Life and Structure Integrity
Phenomenological Approach (Based on S-N curves)
Fatigue Crack Growth (Based on Fracture Mechanics)
Estimation of Fatigue Limit in Practice (R=-1)
1) From ultimate tensile strength, er = 0.5 u
(First approach, it is n
Fatigue Crack Growth (2)
Fatigue crack growth behavior (initiation and propagation)
Residual strength and damage tolerance
-structure is damage/cracked, but has tolerance
to failure
Paris equation (fracture mechanics approach)
da
(K )m
=C
dN
ISSUES TO
Tough Materials?
Stiff materials?
Strong Materials?
Cheap Materials?
Hard materials?
How to estimate ductility, toughness and hardness of materials?
I. Ductility
f = % EL =
L f Lo
Lo
x100
Adapted from Fig. 6.13,
Callister 6e.
Ao A f
Another ductility me
Fatigue Failure of Materials
What is fatigue?
What is its implication?
De Havilland Comet 1
Fatigue: a process of
damage and failure due
to cyclic loading.
80% failure is relevant to
Fatigue.
Annual cost of fatigue to
US economy is 3% of
GNP.
A subject of
Characteristics of Fracture Toughness
At fracture
K = KC
At yield
Is Kc constant?
= c
Dependent on
load, geometry
of structure, and
defect size
Kc is the critical stress
intensity factor at
fracture.
When is Kc constant?
Dependent on
materials
microstruc
Fatigue Crack Growth
How to achieve damage tolerance design
ISSUES TO ADDRESS.
Mechanisms of fatigue Failure
Fracture mechanics approachParis equation
Evaluation of crack growth rate
S-N curves
(Stress amplitude (sa) versus life (Nf) curves)
Three basi
Fatigue of Notched Members
Effects of Notches
Fatigue Notch Sensitivity
How to describe it
Interpretation of S-N Curve
Fatigue Strength Sa
(at a certain life time)
Fatigue Limit
(or Endurance Limit)
Steam Turbine Rotor with Blades
Fatigue Crack
Shaft o
Youngs Modulus and Yielding Stress
For a particular metallic alloy
can we increase its Youngs modulus?
can we increase its yielding stress?
How do sand particles stay together?
How do individual atoms stay together?
At the Atomic Scale
Primary Chemical
Effect of Mean Stress
Fatigue Limit (Endurance Limit)
Effect of Mean Stress (Stress Ratio)
Variable Amplitude Loading
Fatigue Life Predication
S
a2
a1
Nf2
Nf1
N
S-N curves
(Stress amplitude (sa) versus life (Nf) curves)
Three basic types (Sm=0):
a C D
Creep and Creep Failure
How Long a Material Can Sustain at
Elevated Temperatures Before Rupture?
Power-law Creep
Effect of Combined Fatigue and Creep Loads
CREEP
Characteristics
It is stress-dependent and
temperature-dependent!
Stress Versus Temperature f
Failure Criteria
How does a material fail under the multiple stresses?
ISSUES TO ADDRESS.
failure criteria in terms of yielding and brittle failure
how to select failure criteria
Uniaxial Stress
Ductile
Brittle
> c
Triaxial Stresses
Does the material
y
Yielding Stress/Strength
For a particular metallic alloy
can we increase its Youngs modulus?
can we increase its yielding stress?
Elastic-Perfectly Plastic
Most commonly used model in design and analysis!
The material takes a only constant stress (= yie
Case Studies in Modulus-limited Design
Will discuss two examples in the text book
Flow of Stress/Load
How to define the amount in individual branches?
Load is distributed upon stiffness
How is the load distributed?
F
Statics
E1>E2>E3
E1
F1=?
E3
F2=?
E2
F3
A brief review on
Fundamentals of Materials and
Structural Mechanics (2)
Beams
A beam is a structural element that
is capable of withstanding load
primarily by resisting bending. The
bending force induced into the
material of the beam as a result of
the
Fracture Criterion
STRESS CONCENTRATION DUE TO DEFECTS
Elliptical hole in
a plate:
Stress distrib. in front of a hole:
Stress conc. factor:
Large Kt promotes failure:
Kt-stress concentration
factor
o-remote applied stress
Stresses at the Crack Tip
KI
1-,2-,and 3-Dimensional (3-D) Stress and Strain
States
Thermal Stresses /Thermal Shock
Three-dimensional Stress State
xy=yx
xz=zx
yz=zy
Why?
Only Six Independent Stress Components!
Free Surface:
z
y
x
z=zx=zy=0
Plane-Stress State
X
Y
x
Generalised Hookes
Basic Mechanical Property
of Materials
A Tensile Test
What did you measure for a tensile test?
A Load-Displacement Curve
=F/A
The stress
always has a
unit, normally
MPa
Strain:
(Engineering Strain)
or
(True Strain)
A Stress-Strain Curve
Modulus of Elastic
MECH5362 Materials II
Guideline for Report
Every two students work as a group (see the separated group list) to
submit a report (of five A4 pages maximum, exclusive of cover page) on a
particular engineering material after searching and studying, addressi
Why does the thing get loose?
Stress level is below o
A Tensile Test
Loading Rate?
Displacement Rate?
1 mm/mm
5 mm/min
1 m/min
Normally both the elastic modulus and yielding strength
increase with the loading rate
Viscoelasticity
Creep
Recovery
Relaxation
Rules of Mixtures
E X = EmVm + E f V f
Parallel Model
EY =
E f Em
Vm E f + V f Em
G XY =
Series Model
G f Gm
VmG f + V f Gm
v X = v f V f + vmVm
Void content = 0!
Vm + V f = 1
1) Elastic modulus-Longitudinal Direction
Substrates:
f-fibre
m-matrix
cl-compo
Some Useful Points in Design and Analysis
Specific Stiffness and Specific Strength
Specific Stiffness Elastic modulus to weight ratio,
i.e. /
Specific strength strength to weight ratio, i.e. f /
Dyneema and Spectra are synthetic fibers of UHMWPE fibres,
Fracture Failure
Why Fracture (Not Yield)?
An event involving propagation of a crack (or cracks)
July 27, 2009
AIRCRAFT engineers have
demanded Virgin Blue
inspect its entire plane fleet
after reports that a wheel
disintegrated on a plane as
it landed at
Composites Materials
How do we estimate properties of composite?
Compounds?
Blends?
Alloys?
Any material made of two or more than two constituents
in macroscopic (or most recently microscopic or nano)
scale!
More Frequently refers to fibre-matrix composi
MECH 3362 Materials II
(Introduction)
Learning Commitments
There are three lectures per week
Prof Lin Ye
Tutorials
Each student enrolled goes to one of the 3 classes, following
the individual timetable. Stay in one class in the whole
semester
*No tutorial
Leak Before Break
Leak Before Break
*Pressure vessels should be designed to leak before they fracture,
i.e. Cc > t or t < Cc (if KIC and stress are known).
Yielding against Brittle Fracture
Sc =
Kc
a
Yielding against Brittle Fracture
Sc =
Kc
a
Yielding ag
Three-dimensional Stress State
The arrows indicate the positive direction!
Principal Stresses? What are they and why?
How to define them?
3
Why is it 45-degree
x
x
1 = x cos 2
2 = x sin 2
12 = x sin cos
Shear slip normally in a plane 45-deg to the