Fatigue Life Prediction for Elastomers - Axel · PDF fileAbout Endurica –The Company...

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


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


Developing a Rubber Component


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)


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


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


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


Variable Amplitude Results

Natural Rubber SBR


Cadwell’s Test Specimen

1

2


1

2

Specimen under lateral

compression


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


-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


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


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


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.

Fatigue Life Prediction for Elastomers - Axel · PDF fileAbout Endurica –The Company...

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