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Task 6 - Safety Review and LicensingOn the Job Training on Stress Analysis
Pisa (Italy)June 15 – July 14, 2015
Static strength and High and Low-Cycle Fatigueat room temperature 1/2
Davide Mazzini – Ciro Santus
2
Teaching
Fundamental of Machine Design (Bachelor, Mechanical Engineering)
Computer-Aided Engineering, FE (Master, Mechanical Engineering)
Research
Fatigue of Materials and Structures
Contact Mechanics
Dynamics
…
Pisa, June 15 – July 14, 2015
Prof. Ciro Santus
3Pisa, June 15 – July 14, 2015
My latest paper – Eng. Fr. Mechanics, Elsevier
Flange leakage pressure deduced from a Weight Function application
Validations:- FE- Exper.
4Pisa, June 15 – July 14, 2015
Other paper – Eng. Fr. Mechanics, Elsevier
Analytical/ Numerical procedure to calculate the Stress Intensity Factors for Rolling Contact Fatigue
FE validation
5
Content
• Static strength of metals, Ductile/ Brittle
- Tensile test
- Plastic collapse vs. Brittle fracture notched components
• Fatigue of metals
- Stress/ Strain approaches
- Low/ High Cycle Fatigue
- Fatigue notch sensitivity
Table of content – Class VI.a.1
Pisa, June 15 – July 14, 2015
6
Books on Material mechanical properties
W. D. Callister, D. G. Rethwisch. Fundamentals of Materials Science andEngineering An Integrated Approach. Wiley 2007.
N. E. Dowling. Mechanical Behavior of Materials. Prentice Hall 1999.
Books specifically on Fatigue
S. Suresh. Fatigue of Materials. Cambridge University Press 1998.
H. E. Boyer. Atlas of Fatigue Curves. ASM International 2003.
… and many many others
Books
Pisa, June 15 – July 14, 2015
7
Metals
FCC – Face Centered Cubic BCC – Body Centered Cubic
Pisa, June 15 – July 14, 2015
Most usual metal crystal structures
8
Dislocation mechanics
Metals
The dislocation mobility is the basic for
Metals ductility
Pisa, June 15 – July 14, 2015
9
Dislocation interactions
Other dislocation previousy accumulated → work hardening
Other defect → alloy composition
Grain boundaries → heat treatment
Dislocation Mechanics
Pisa, June 15 – July 14, 2015
10
Static, quasi-static, or monotonic tests
Tensile tests
Hardness tests
Fracture Toughness tests
Charpy tests
… and others
Mechanical tests on materials
Pisa, June 15 – July 14, 2015
11
Specifications
Uniform section of the specimen
Imposed constant (low) Strain rate up to fracture
Measurements:
Load Cell and
Extensometer Displacement
Material properties tested
Bulk strength “without any gradient” (unnotched specimen)
Ductility up to fracture
Tensile test
Pisa, June 15 – July 14, 2015
12
ASTM Standard E8/E8M – 11
Definition of the test, specimen sizes, recommendations, etc.
Tensile test
Pisa, June 15 – July 14, 2015
13
ASTM Standard E8/E8M – 11
Specimen:
- Flat specimen
- Round specimen
Tensile test
Pisa, June 15 – July 14, 2015
14
ASTM Standard E8/E8M – 11
Specimen:
- Flat specimen
- Round specimen
Tensile test
Most used
20 0
Initialsection and lenght:
,4
A D L G
Pisa, June 15 – July 14, 2015
15
Tensile test
Linear elasticbehavior
Elastic-plastic,post yield
YS
0.2%
US
FS
NeckingPost necking
Final Fracture
0
LL
F
Pisa, June 15 – July 14, 2015
0
FA
16
Tensile Test – definitions
0
0
Y U F
F
Load as measured by the load cellElongation as measured by theextensometer
Engineeringstress
Engineeringstrain
(before yield) Young's modulus
, , Yield, Ultimate, Fracture strength valuesEl
FL
FAL
L
E
S S S
ongation at Fracture (usually in %)
Pisa, June 15 – July 14, 2015
17
Tensile Test – definitions
Yield point
Low-carbon steel, C 0.05-0.15%Mild/ high-carbon steel, C≥0.2%And all the other metals
Yield point
Conventional Yield(at 0.2% offset)
0.2%
Line parallelto the elastic
Pisa, June 15 – July 14, 2015
18
Tensile Test – True curve
Engineering/ True curve
0 0
, Engineering, True
Ais thecurrent area
d+...=
Before necking:(1 )ln(1 )
FAL L L
L L L L
Pisa, June 15 – July 14, 2015
19
Tensile Test – True curve
After necking
is no more uniform,the test redportio
uces to aof thesp nn ecime
A
A
Pisa, June 15 – July 14, 2015
20
Tensile Test – True curve
True curve Stress/ Strain at final fracture
f
0F F
F
0F
F
F
0 F
0
At least at fracture is known:
ln
Instead of ,Reduction of Area
% 100
AASA
AA
A ARAA
f
(measuredafter fracture)
A
Pisa, June 15 – July 14, 2015
21
Example
0 5 10 150
200
400
600
800
1000
1200
Strain, %
Stre
ss, M
Pa
exp. data0.2% Yield line0.2% Yield StrengthUltimate Tensile StrengthFracture
AISI 4340, Engineering
E
F F,S
US
YS
Pisa, June 15 – July 14, 2015
22
0 10 20 30 40 50 600
200
400
600
800
1000
1200
1400
Strain, %
Stre
ss, M
Pa
EngineeringTrue
Example
AISI 4340, True
F F,
Linear interpolationfrom Necking pointto Fracture point
Pisa, June 15 – July 14, 2015
23
Homework
Write a MATLAB script to find both Engineering and True curve
and find the Stress and elongation parameters
Pisa, June 15 – July 14, 2015
24
YouTube video
https://www.youtube.com/watch?v=NrIErdXvjRQ
Pisa, June 15 – July 14, 2015
25
Why does the Necking happen?
SU is not a strength parameter, Necking is a point of instability onset
d d dd d d
At necking d / d 0 :d dd d
After necking d /predominant until fr
d is
thusact
d 0ure
d /
F AF AAt t t
F tAA
t tA t
F t
Positive Negative
Weakest linkIt goes into NeckingChain model of the
tensile specimen
The other links experience unloadingbefore reaching their necking condition, so necking does not extend to the stronger links
Pisa, June 15 – July 14, 2015
26
Necking on the entire specimen
Other materials (not metal) may have necking distributed
on the entire specimenAt necking d / d 0 :d dd d
After necking d / d is predominantthus the load drops, but
db
predomin
efore fracture, becomesd
again so neckingextends to the entire speci
ante
m n
F tAA
t tA t
t
Pisa, June 15 – July 14, 2015
27
Tempering after quenching at different temperatures (Es. AISI 4340)
Steel - Different mechanical properties
Pisa, June 15 – July 14, 2015
28
Hardness tests
Resistance to the penetration / scratch
Different mechanical properties
Pisa, June 15 – July 14, 2015
29
Different mechanical properties
Pisa, June 15 – July 14, 2015
30
Hardness tests
Differences with respect to the Tensile test:
• Compressive rather than Tensile
• Plastic deformation and No fracture
• Multiaxial (stress) instead of Uniaxial
• Small surface portion of material instead of
bulk material
• Result dependent on the Standard definition
of load and indenter size
Different mechanical properties
U
Nevertheless alinear relationshipis remarkably accurate(only for steels):
3.45HBS
Pisa, June 15 – July 14, 2015
31
Metals can be (broadly) distinguished into:
- Ductile, elongation at fracture > 5%
- Brittle, elongation at fracture < 5%
Usually brittle metals do not
reach the Necking
Ductile - Brittle
0 1 2 3 4 50
500
1000
1500
2000
2500
Strain, %
Stre
ss, M
Pa
Example: Quenched steel
F F,S
Pisa, June 15 – July 14, 2015
32
Different criteria for Ductile/ Brittle metals
- Ductile:
- Plastic collapse
- Ductility exhaustion
- Brittle:
- Fracture
Ductile - Brittle
Pisa, June 15 – July 14, 2015
33
Notched geometry
Stress Concentration – Force flux
Central hole in a plate
Stress concentrates at the notch apexeither a circle or any other concave shape
Pisa, June 15 – July 14, 2015
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Notched geometry
n 0
max
maxt
Nominalstress: , , (force/area)
Maximumstress: (peak value)
SCF:
K
Stress Concentration Factor
Central hole in a plate
Pisa, June 15 – July 14, 2015
35
Notched geometry
maxtK
Stress Concentration Factor
Central hole in a plate
Pisa, June 15 – July 14, 2015
36
Notched geometry
Stress Concentration Factor
Many tables and graph for several cases
Pisa, June 15 – July 14, 2015
37
Ductile metal
Plastic collapse
Elastic perfectly plasticallyModel
Different stagesof the load
F
timePlasticity onset
Plastic collapse
ab
cd
Pisa, June 15 – July 14, 2015
38
Ductile metal
Plastic collapse
YF ASAt plastic collapse the ultimate force does not depend on theStress Concentration Factor
Pisa, June 15 – July 14, 2015
39
Ductile metal
Ductility exhaustion
The fracture could happen before the Plastic Collapse, if the strain reaches the (true) elongation at fracture
max
F
max F ?
How tocalculate ?
Plasticity zone spreading out
Fracture for ductility exhaustion
Pisa, June 15 – July 14, 2015
40
Ductile metal
The Neuber’s rule (1946)
, el el
tt
2t( )
nominalstress
K SK SE
K SE
S
After imposing equal the (triangular) areas it follows:
Any kind of (radiused)notch
el el,
Pisa, June 15 – July 14, 2015
41
Ductile metal
The Neuber’s rule (1946)
2t( )K SE
ElastAny ma
ic peterial mode
rfectly plla, suchsti
ascally
Neuber’shyperbola
YS
Pisa, June 15 – July 14, 2015
42
Ductile metal
Plastic collapse/ Neuber’s rule example
Y
t
Steel Fe360-S235235MPa
205GPa% 50%
5.0(anyshape)
SERAK
Plas
Byin
tic
creasing
collapse
the load,what happ
Ductility e
ens first:or
xhaustion?
Pisa, June 15 – July 14, 2015
43
Ductile metal
Plastic collapse/ Neuber’s rule example
Y
t
Steel Fe360-S235235MPa
205GPa% 50%
5.0(anyshape)
SERAK
F
Y
2t
max max
1ln 0.691 % /100
Assuming to have plastixccollapse first:
Neuber:
RA
S
KE
Pisa, June 15 – July 14, 2015
44
Ductile metal
Plastic collapse/ Neuber’s rule example
Y
t
Steel Fe360-S235235MPa
205GPa% 50%
5.0(anyshape)
SERAK
max Y
max2t Y
max
max F
then,assuming elastic prefectlyplastic material model:
finally, can besolved:
0.029
beingplasticcollapse happens first
S
K SE
Pisa, June 15 – July 14, 2015
45
Ductile metal
Plastic collapse/ Neuber’s rule example
Y
t
Steel Fe360-S235235MPa
205GPa% 50%
5.0(anyshape)
SERAK
Y F
t
Homework:1.What if a different steel is considered:
1700 MPa and 0.08
2.Which is the(minimum) to haveductilityexhaustion first?
S
K
Pisa, June 15 – July 14, 2015
46
Brittle metal
The maximum stress just induces fracture
0 1 2 3 4 50
500
1000
1500
2000
2500
Strain, %
Stre
ss, M
Pa
F F,S
max t F
Fracture:K S
No more margindue to ductility
The SCF has a direct effect on fracture.Ductile metals are usually preferred than Brittle
Pisa, June 15 – July 14, 2015
47
Ductile/ Brittle metal
Different levels of stress concentration severity
Ductile,blunt notchPlasticcollapse
Brittle,blunt notchFracture
Ductile,sharp notchPlasticCollapse orDuctility exhaustion
Brittle,sharp notchFracture
tK
tK
tK
tK
Ductile,Crack notchHow to predict the strength?
Brittle,Crack notchHow to predict the strength?
tK
tK
r r 0
Pisa, June 15 – July 14, 2015