fatigue life prediction for elastomers - axel · pdf fileabout endurica –the company...
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EnduricaAccelerating Reliable Design
Fatigue Life Prediction
for Elastomerswww.endurica.com
About Endurica – The Company
• LLC Founded in March 2008
• Vision– Make fatigue life prediction of elastomers as widely practiced and well-understood as
fatigue life prediction of metals.
– Materials, component, and system developers will have capable, reliable, proven methods for assessing fatigue life.
• Mission– Provide services, technology, and training that accelerate reliable design for elastomer
materials and components.
– Empower practitioners with knowledge, methods, tools for fatigue analysis.
• Technology– We develop and apply the Endurica fatigue life prediction code - a patented,
proprietary system for analyzing the effects of multiaxial, variable amplitude duty cycles on elastomers.
© 2008 Endurica LLC
About Endurica –Business Model
© 2008 Endurica LLC
Consulting Training
Technology
Licensing
Analysis Services
About Endurica – The Code
• Interface– text file input and output
– DOS command line execution
• Fatigue life prediction code for rubber– Patented plane-specific algorithm
– Stress-strain, fatigue laws applicable to rubber
• V1.0 – 2000 – initial implementation of plane-specific algorithm
• V1.5 – 2001 – first release for production use
• V2.1 – 2006 – wider selection of material models, easier inter-use with ABAQUS
• V2.17 – current release
• Investment to Date– 3 solid man-years code development
– 4 man-years code validation
– 1 Patent
– 2 PhD theses
– Publications: 25+ (most cited on topic “rubber fatigue”, according to Google scholar)
– Joint Industry Program with international partners in automotive OEM business
• Current State– Thousands of analyses completed: tires, mounts, lab specimens, medical devices
– Small user base
– Business decision - offer as a service, initially
• Working with a small number of customers – “word of mouth”– Automotive OEM, OEM supplier, medical devices, energy
© 2008 Endurica LLC
Developing a Rubber Component
© 2008 Endurica LLC
Industry Sectors:
•Medical devices
•Automotive
components
•Energy (Oil and Gas)
•Consumer products
•Military
•Aero
Analysis Paradigm 11
22
12
033
11
22
12
033
Fatigue Life Prediction
Mate
rial P
ropert
ies
Because of their macromolecular structure,
elastomers exhibit unique behavior and require
specialized analysis methods.
Endurica is the first commercially available
fatigue life simulation that addresses the
unique characteristics of elastomeric
materials.
Given the material properties and duty cycle of
a rubber component, the number of cycle
repeats that will be endured before fatigue
failure can be computed.
Endurica considers the factors that distinguish
elastomers:
•Finite Strains
•Nonlinear Elasticity
•Strain Crystallization
•Time Dependence
Crack Driving Force
Cra
ck g
row
th r
ate
Duty
Cycle
Nom
inal S
train
Time
11
22
12
•Temperature Dependence
•Ozone Attack
•Mullins Effect
Analysis Issues
0 0.2 0.4 0.6 0.8 1
Applied to Structure
Fraction of Mission Profile
Load / D
ispla
cem
ent
0 0.2 0.4 0.6 0.8 1
Experienced by Crack
Fraction of Mission Profile
Cra
ck D
rivin
g F
orc
e
Material Characterization
Life Calculation Scheme
),( r
( ), ( )ij ijt t
0
1( , )
( , )
fc
f
c
N dcf T R
( , )
dcf T R
dN
-1
-0.5
0
0.5
1
-1-0.8-0.6-0.4-0.200.20.40.60.81
0
0.2
0.4
0.6
0.8
1
min min ,min, , fN
FEA
F(t)
Equivalence
Parameter(Loading Conditions
Experienced on a
material plane)
Energy Release Rate(Loading Conditions Experienced on at
Crack Tip)
© 2008 Endurica LLC
Deals with:
•Crack closure
•Multiaxiality
•Critical plane
•Nonlinear elasticity
•FCG behaviors
unique to
elastomers
US Patent No. 6,634,236 B1
Validation Experiences
Axial / Shear Fatigue Experiments
Mars, W.V., Fatemi, A., 2004. A Novel Specimen for
Investigating Mechanical Behavior of Elastomers under
Multiaxial Loading Conditions, Experimental Mechanics, 44:
136-146.
Test Specimen
NR + 60 phr N650
© 2008 Endurica LLC
Loading Paths Investigatedθ
δ
A θ
δ
B θ
δ
C
θ
δ
D θ
δ
Fθ
δ
E
θ
δ
G θ
δ
H θ
δ
I
Multiaxial Fatigue of Rubber, W. V. Mars, Ph. D. Dissertation, University of Toledo, 2001. © 2008 Endurica LLC
Cracking Plane Observations
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Predicted Failure Plane, deg
Ob
serv
ed
Failu
re P
lan
e, d
eg
Path A Path B Path C Path D1
Path D2 Path E Path F Path L
Path G Path H Path I
B
A
C
J
K
E
D
F
G
H
I
© 2008 Endurica LLC
Multiaxial Fatigue Life Correlation
0.01
0.1
1
10
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Nf
Pe
ak
CE
D,
MP
a
Path A Path B Path C Path D1
Path D2 Path E Path F Path G
Path H Path I Path J Path K
Path L Path M Path N Path O
Nf = 16100 (Wc,max)-2.15
r2 = 0.78
Variable Amplitude Test Signals
• Signals vary R-ratio, load severity, and load
sequence in a repeated block format
© 2008 Endurica LLC
Variable Amplitude Results
Natural Rubber SBR
© 2008 Endurica LLC
Cadwell’s Test Specimen
1
2
Cadwell’s Test Specimen
1
2
Specimen under lateral
compression
Cadwell’s Test Specimen
1
2
Specimen under lateral
compression and shear.
Experimental Results
• Loading
– Compression / Tension
– Cyclic Shear
• R Ratio
– Fully Relaxing (R = 0)
– Non-Relaxing (R > 0)
• Long Fatigue Life
– Threshold Effects
– Ozone attack
COMPLEX!
Finite Element Analysis
•10 x 10 x 10 mesh
•3-D, 2nd order,
hybrid formulation,
reduced integration
elements
(C3D20RH)
•Neo-Hookean
constitutive model,
C10 = 0.5 MPa
•Sinusoidal Cyclic
Shear Loading
•Strain History
Recovery: Element
Centroids
Finite Element Analysis
G
H
I
D
E
F
A
B
C
Edge View Front View
1.E-12
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05
Maximum Energy Release Rate, J/m2
Fa
tig
ue
Cra
ck
Gro
wth
Ra
te, m
/cy
c
R=0
R=0.05R=0.10
Crack Growth Properties
Tc = 10 x 103 J/m2
rc = 5 x 10-3 mm/cyc
F = 2
Tt = 450 J/m2
T0 = 100 J/m2
rz = 8 x 10-9 mm/cyc
C = 7
( ) CRF R Fe
Tc
T0
Tt
F
rc
rz
c0 = 0.02 mm
cf = 1.00 mm
Results
I
CGD
A
HFE
B
1.00E+05
1.00E+06
1.00E+07
1.00E+08
1.00E+09
1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+09
Predicted Life
Rep
ort
ed E
xp
eri
men
tal L
ife
Material Characterization
Stress-Strain Behavior
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
Simple Uniaxial
Pure Shear
Equibiaxial
L
3MPa
4
G
5
1
122)3(
i
ii
i
m
i IC
GW
Arruda-Boyce
potential
Effect of Strain Crystallization on
FCG Rate
R. Harbour, A. Fatemi, W. V. Mars, Fatigue and Fracture of
Engineering Materials and Structures, vol. 30, pp. 640-652, 2007.
Typical Computed Haigh Diagram
Match to known behavior
Comparing Haigh Diagrams
Control
No
Crystallization
Comparing Cadwell Diagrams
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
-0.5 1.5 3.5 5.5
Minimum Strain
Fatigu
e L
ife
Duty cycle analysis
Multiaxial Input
© 2008 Endurica LLC
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50 60 70 80 90 100
Time, sec
No
min
al
Str
ain
11
22
12
Identification of Critical Plane
3
3.5
4
4.5
5
5.5
6
0 45 90 135 180
Log1
0(F
atig
ue
Lif
e)
Crack Orientation, deg
Crack Plane Experience
© 2008 Endurica LLC
0.00E+00
2.00E+05
4.00E+05
6.00E+05
8.00E+05
1.00E+06
1.20E+06
1.40E+06
1.60E+06
1.80E+06
0 200 400 600 800 1000
Cra
ckin
g E
nerg
y D
en
sit
y,
Pa
Time, sec
Rainflow Count Results – Peak and
R ratio for each event
© 2008 Endurica LLC
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.00E+00
5.00E+05
1.00E+06
1.50E+06
2.00E+06
2.50E+06
3.00E+06
0 50 100 150 200 250
R R
atio
Pe
ak C
ED,
Pa
Event, sorted from most damaging to least
Peak CED
R Ratio
Damage Rate, by event
© 2008 Endurica LLC
1.E-11
1.E-09
1.E-07
1.E-05
1.E-03
1.E-01
0 50 100 150 200 250
FCG
R,
m/c
yc
Event, sorted from most damaging to least
Note: Crack growth rates are evaluated at the initial flaw
size
N
i
ci RWrr1
max, ),(
Construction of Abbreviated
Strain History
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
0 45 90 135 180
Fati
gue
Lif
e, c
ycle
s
Crack Orientation, deg
M=1
M=2
M=4
M=8
M=16
M=32
M=64
Full cycle
-0.5
-0.25
0
0.25
0.5
0 200 400 600 800 1000
Stra
in11
22
12
Endurica Distinguishers
• Addresses unique aspects of elastomers
– Hyperelasticity / finite straining
– Strain crystallization
– Mullins effect
– Time-dependence
• Advanced fatigue simulation methods
– Critical plane
– Rainflow
– Crack closure
• Founded on a large body of experimental validation work
• Efficient material characterization
Our Analysis Services
• Material Characterization
– We determine the parameters needed to represent your materials in our analysis process,
and generate plots showing computed response over a range of conditions.
• Fatigue Life Prediction
– We apply our patented analysis process to show how your materials will endure under your
given duty cycles. Our specialty is accounting for the effects of multiaxial, variable amplitude
strain histories, as you might determine via Finite Element Analysis or experiment. We can
efficiently analyze duty cycles from every element in a finite element model to locate the
point of minimum fatigue life.
• Failure Site Analysis
– Our analysis can show which planes are likely to develop cracks, and how the applied strain
history is transformed into the localized experience of the failure site.
• Duty Cycle Analysis
– Our analysis can identify the events that contribute most to crack development. This enables
developers to focus design mitigation efforts on the most critical loading conditions, test
engineers to compress the duty cycle while retaining relevance to actual service conditions.