Task 6 - Safety Review and Licensing
On the Job Training on Stress Analysis
Static strength and High and Low-Cycle Fatigue
at room temperature 1/2
Davide Mazzini – Ciro Santus
Pisa (Italy)
June 15 – July 14, 2015
Prof. Ciro Santus
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
2
My latest paper – Eng. Fr. Mechanics, Elsevier
Validations:
- FE
- Exper.
Flange leakage pressure
deduced from a Weight
Function application
Pisa, June 15 – July 14, 2015
3
Other paper – Eng. Fr. Mechanics, Elsevier
Analytical/ Numerical
procedure to calculate the
Stress Intensity Factors for
Rolling Contact Fatigue
FE validation
Pisa, June 15 – July 14, 2015
4
Table of content – Class VI.a.1
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
Pisa, June 15 – July 14, 2015
5
Books
Books on Material mechanical properties
W. D. Callister, D. G. Rethwisch. Fundamentals of Materials Science and
Engineering 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
Pisa, June 15 – July 14, 2015
6
Metals
Most usual metal crystal structures
FCC – Face Centered Cubic
BCC – Body Centered Cubic
Pisa, June 15 – July 14, 2015
7
Metals
Dislocation mechanics
The dislocation mobility is the basic for
Metals ductility
Pisa, June 15 – July 14, 2015
8
Dislocation Mechanics
Dislocation interactions
Other dislocation previousy accumulated → work hardening
Other defect → alloy composition
Grain boundaries → heat treatment
Pisa, June 15 – July 14, 2015
9
Mechanical tests on materials
Static, quasi-static, or monotonic tests
Tensile tests
Hardness tests
Fracture Toughness tests
Charpy tests
… and others
Pisa, June 15 – July 14, 2015
10
Tensile test
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
Pisa, June 15 – July 14, 2015
11
Tensile test
ASTM Standard E8/E8M – 11
Definition of the test, specimen sizes, recommendations, etc.
Pisa, June 15 – July 14, 2015
12
Tensile test
ASTM Standard E8/E8M – 11
Specimen:
-
Flat specimen
-
Round specimen
Pisa, June 15 – July 14, 2015
13
Tensile test
ASTM Standard E8/E8M – 11
Initialsection and lenght:
Specimen:
A0 
-
Flat specimen
-
Round specimen

4
D 2 , L0  G
Most used
Pisa, June 15 – July 14, 2015
14
Tensile test
F

A0
SU
Necking
Post necking
Elastic-plastic,
post yield
SF
SY
Final Fracture
Linear elastic
behavior
F
0.2%
Pisa, June 15 – July 14, 2015
L

L0
15
Tensile Test – definitions
F Load as measured by the load cell
L Elongation as measured by the extensometer
F
Engineering stress

A0

L
Engineering strain
L0

E
(before yield) Young's modulus

S Y , S U , SF Yield, Ultimate, Fracture strength values
 F Elongation at Fracture (usually in %)
Pisa, June 15 – July 14, 2015
16
Tensile Test – definitions
Yield point
Conventional Yield
(at 0.2% offset)
Yield point
Line parallel
to the elastic
0.2%
Mild/ high-carbon steel, C≥0.2%
And all the other metals
Low-carbon steel, C 0.05-0.15%
Pisa, June 15 – July 14, 2015
17
Tensile Test – True curve
Engineering/ True curve
 ,  Engineering
 ,  True
F
A is the current area
A
dL
L
L


+...= 

L0
L0  L
L
 
Before necking:
   (1   )
   ln(1   )
Pisa, June 15 – July 14, 2015
18
Tensile Test – True curve
After necking
A
A is no more uniform,
the test reduces to a
portion of the specimen
Pisa, June 15 – July 14, 2015
19
Tensile Test – True curve
True curve Stress/ Strain at final fracture
At least at fracture Af is known:
 F  SF
A0
AF
 A0 
F  ln  
 AF 
Af
Instead of F , Reduction of Area
A0  AF
% RA  100
A0
Pisa, June 15 – July 14, 2015
(measured
after fracture)
20
Example
AISI 4340
 ,  Engineering
1200
SU
1000
SY
Stress, MPa
800
SF ,  F
600
400
exp. data
0.2% Yield line
0.2% Yield Strength
Ultimate Tensile Strength
Fracture
200
0
E
0
5
Strain, %
Pisa, June 15 – July 14, 2015
10
15
21
Example
 ,  True
AISI 4340
1400
 F , F
1200
Linear interpolation
from Necking point
to Fracture point
Stress, MPa
1000
800
600
400
200
0
Engineering
True
0
10
20
30
Strain, %
Pisa, June 15 – July 14, 2015
40
50
60
22
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
23
YouTube video
https://www.youtube.com/watch?v=NrIErdXvjRQ
Pisa, June 15 – July 14, 2015
24
Why does the Necking happen?
SU is not a strength parameter, Necking is a point of instability onset
F   A Positive
dF d
dA
A  

dt
dt
dt
Negative
Chain model of the
tensile specimen
At necking dF / dt  0 :
d
dA

A  
dt
dt
After necking dA / dt is
predominant until fracture
thus dF / dt  0
Weakest link
It goes into Necking
The other links experience unloading
before reaching their necking
condition, so necking does not extend
to the stronger links
Pisa, June 15 – July 14, 2015
25
Necking on the entire specimen
Other materials (not metal) may have necking distributed
on the entire specimen
At necking dF / dt  0 :
d
dA
A  
dt
dt
After necking dA / dt is predominant
thus the load drops, but
d
before fracture,
becomes
dt
predominant again so necking
extends to the entire specimen
Pisa, June 15 – July 14, 2015
26
Steel - Different mechanical properties
Tempering after quenching at different temperatures (Es. AISI 4340)
Pisa, June 15 – July 14, 2015
27
Different mechanical properties
Hardness tests
Resistance to the penetration / scratch
Pisa, June 15 – July 14, 2015
28
Different mechanical properties
Pisa, June 15 – July 14, 2015
29
Different mechanical properties
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
Pisa, June 15 – July 14, 2015
Nevertheless a
linear relationship
is remarkably accurate
(only for steels):
S U  3.45 HB
30
Ductile - Brittle
Metals can be (broadly) distinguished into:
-
Ductile, elongation at fracture > 5%
-
Brittle, elongation at fracture < 5%
2500
Usually brittle metals do not
2000
Stress, MPa
reach the Necking
Example: Quenched steel
SF ,  F
1500
1000
500
0
0
Pisa, June 15 – July 14, 2015
1
2
3
Strain, %
4
5
31
Ductile - Brittle
Different criteria for Ductile/ Brittle metals
-
-
Ductile:
-
Plastic collapse
-
Ductility exhaustion
Brittle:
-
Fracture
Pisa, June 15 – July 14, 2015
32
Notched geometry
Stress Concentration – Force flux
Central hole in a plate
Stress concentrates at the notch apex
either a circle or any other concave shape
Pisa, June 15 – July 14, 2015
33
Notched geometry
Stress Concentration Factor
Central hole in a plate
Nominalstress: ,  n ,  0 (force/area)

Maximum stress: max (peak value)
SCF:
 max
Kt 

Pisa, June 15 – July 14, 2015
34
Notched geometry
Stress Concentration Factor
Central hole in a plate
 max
Kt 


Pisa, June 15 – July 14, 2015
35
Notched geometry
Stress Concentration Factor
Many tables and graph for several cases
Pisa, June 15 – July 14, 2015
36
Ductile metal
Plastic collapse
Different stages
of the load
F
d
b
c
a
time
Elastic perfectly
plastically
Model
Plasticity onset
Plastic collapse
Pisa, June 15 – July 14, 2015
37
Ductile metal
Plastic collapse
F  A SY
At plastic collapse the ultimate
force does not depend on the
Stress Concentration Factor
Pisa, June 15 – July 14, 2015
38
Ductile metal
Ductility exhaustion
The fracture could happen
before the Plastic Collapse,
if the strain reaches the
(true) elongation at fracture

Fracture for ductility
exhaustion
 max
F
Plasticity zone
spreading out

 max  F ?
How to
calculate  ?
Pisa, June 15 – July 14, 2015
39
Ductile metal
The Neuber’s rule (1946)
Any kind of (radiused)
notch
 el ,  el
 ,
After imposing equal the
(triangular) areas it follows:
 el el  
Kt S
 
E
( K t S )2
 
E
Kt S
S nominalstress
Pisa, June 15 – July 14, 2015
40
Ductile metal
The Neuber’s rule (1946)
Any material model, such as
Elastic perfectly plastically
SY
Neuber’s
hyperbola
Pisa, June 15 – July 14, 2015
( K t S )2
 
E
41
Ductile metal
Plastic collapse/ Neuber’s rule example
Steel Fe360-S235
SY  235 MPa
E  205GPa
RA%  50%
K t  5.0 (any shape)
By increasing the load,
what happens first:
Plastic collapse or
Ductility exhaustion?
Pisa, June 15 – July 14, 2015
42
Ductile metal
Plastic collapse/ Neuber’s rule example
Steel Fe360-S235
SY  235 MPa
F  ln 
E  205GPa
RA%  50%
K t  5.0 (any shape)
Assuming to have plastixc collapse first:
  SY
1


  0.69
 1  RA% /100 
Neuber:
 max max
K t 


2
E
Pisa, June 15 – July 14, 2015
43
Ductile metal
Plastic collapse/ Neuber’s rule example
Steel Fe360-S235
SY  235 MPa
E  205GPa
RA%  50%
K t  5.0 (any shape)
then, assuming elastic prefectly
plastic material model:
 max  SY
finally,  max can besolved:
K t2 SY
 0.029
 max 
E
being  max  F
plastic collapse happens first
Pisa, June 15 – July 14, 2015
44
Ductile metal
Plastic collapse/ Neuber’s rule example
Steel Fe360-S235
SY  235 MPa
E  205GPa
RA%  50%
K t  5.0 (any shape)
Homework:
1.What if a different steel is considered:
S Y  1700 MPa and F  0.08
2.Which is the (minimum) K t to have
ductility exhaustion first?
Pisa, June 15 – July 14, 2015
45
Brittle metal
The maximum stress just induces fracture
Fracture:
 max  K t  SF
The SCF has a direct
effect on fracture.
Ductile metals are
usually preferred
than Brittle
2500
No more margin
due to ductility
Stress, MPa
2000
SF ,  F
1500
1000
500
0
0
Pisa, June 15 – July 14, 2015
1
2
3
Strain, %
4
5
46
Ductile/ Brittle metal
Different levels of stress concentration severity
Ductile,
blunt notch
Plastic
collapse
r
Kt 
Brittle,
blunt notch
Fracture
Ductile,
sharp notch
Plastic
Collapse or
Ductility
exhaustion
Brittle,
sharp notch
Fracture
Kt 
Kt 
Ductile,
Crack notch
How to
predict the
strength?
Kt 
Brittle,
Crack notch
How to
predict the
strength?
r
Pisa, June 15 – July 14, 2015
 0
Kt  
Kt  
47