ferenc kun and zolt án halász department of theoretical physics university of debrecen, hungary

03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue fracture

Ferenc Kun and Zoltán Halász

Department of Theoretical PhysicsUniversity of Debrecen, Hungary

Crackling noise in fatigue fracture

of heterogeneous materials

J. S. Andrade Jr. and H. J. HerrmannComputational Physics, IfB, ETH, Zürich, Switzerland

Experiments: fatigue tests of heterogeneous materials

Theoretical approach: fiber bundle model for fatigue

Microscopic failure process: crackling noise

03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

Fatigue-life tests

0

0

Accumulation of deformation

Number of cycles to break (lifetime)

Crack parallel to load

Experiments with asphalt

t

0 c

Sub-critical periodic loading

No instantaneous failure

Complex time evolution

c 0

Disordered micro-structure :c Fracture strength

(Experiments by Jorge Soares, Univ. Fortaleza, Brasil)


Experimental resultsBasquin-lawEvolution of deformation

Immediatebreaking

Power lawIncreaseof lifetime

4.0/0 c 3.0/0 c

cfN

0~

fN

07.02.2

Origin of Basquin-law? Microscopic failure process?

fN


Fiber bundle model for fatigue

Discrete set of parallel fibers on a regular lattice

Range of load redistribution

Two extremes:

Load parallel to fibersF

Perfectly brittle behaviour

E

Two parameters: E, pth

Distribution of failure thresholds

)( thpgthp

p

GLS LLS


Microscopic failure mechanism

Immediate response, breaking when ithi pp

Breaking due to damage accumulation

ttpac )(0

Nucleation rateof microcracks

t

dttpatc0

0 ')'()(

Dependence on loading history

ithi ctc )(

),( thth cph Joint distribution

Healing of damage t

tt dttpeatc0

/)'(0 ')'()(

limits the range of memory

Failure due to two physical mechanisms

Independent breaking thresholds )()(),( thththth cfpgcph


Equation of motion in GLS

)())]((1)][')'((1[0

/)'(00 tptpGdttpeaFt

tt

Parameters: ,0a,

Static FBMDamage accumulationand healing

Initial condition: 000 )](1[ ppG 0p

)(tp

Integral equation:

,0

c

)()( tEtp

deformation

Quasi-static limit: 0 Suppress damage


Time evolution-constant load

)()( tEtp for variousc

0

monotonically increases

Finite lifetime ft

)(t

c 0

ft

Diverging derivative

dt

dfor ftt

Larger smaller

Agreement with the experiments


Lifetime-number of cycles to break

ft as a function of c

0

Different disorder distributions

Different exponents

cft

0~

where

Independent of the typeof disorder

Lifetime Power law behavior

Basquin-law


Loading at a constant

07.1

25.2

Varying and

Rapid failurePower law regime

Agreement with experiments

l

:l fatigue limit


Microscopic process of failure in GLS

02.00 c

Low load value

Long waiting times

Burst mainly at the end

Long damage sequences

Red: immediate breaking

Green: damage


Microscopic process of failure

92.00 c

High load value

Short waiting times

Strong bursting activity

Short damage sequences


Crackling noise in fatigue

Burst size

Waiting time

Damage sequence

Fluctuations

Slow damage sequencesTrigger immediate bursts

::d

:T

Bursts size

Damage sequence

Waiting time

Separation of time scales


Universal power law behaviour

GLSP ~)(

2/32/5 GLS

Burst size distributions

Crossover

c 0for


Damage sequence

ddddP /exp~)( 1

10~ d

TTTTP /exp~)( 1

)1(0~ T

Waiting time

Distributions-Scaling

Universal power laws


Localized load sharing

Load redistribution over nearest intact neighbours

Stress concentration

Enhanced

Damage accumulationImmediate breaking

Bursts

Growing clusters-cracks


Burst size distribution

LLSP ~)(

05.08.1 LLS

Power law distributions

for c 0

2/9LLS


Waiting time distributions

LLSTTP ~)(

GLSLLS Failure processgets faster

for c 0

07.04.1 LLS

Crossover to exponential

Power law distributions


Cluster size distribution

SSP ~)(

Power law behaviour

07.00.2

01.0/ ctt

8.0/ ctt

Growth and merging of clusters


Conclusions

F. K., et al, J. Stat. Mech.:Theor. Exp. P02003 (2007).F. K., et al, Phys. Rev. Lett. 100, 094301 (2008).

Fiber bundle model of fatigue with GLS and LLS

Macro-scale

Reproduces Basquin law

Scaling law of deformation

Micro-scale Crackling noise - bursts triggered by damage

Universal power law distributions

Spatial and temporal correlations

Many open questions

ferenc kun and zolt án halász department of theoretical physics university of debrecen, hungary

Documents

fiber bundle model of

glslow load valuelong

immediate breakinggreen

endlong damage sequencesred

gls parameters

switzerland experiments

lls macroscale

deformationquasistatic