Diapositive 1

Laurent PonsonInstitut Jean le Rond dAlembertCNRS Universit Pierre et Marie Curie, ParisFrom microstructural to macroscopic properties in failureof brittle heterogeneous materials

Good morningI would like to present you this recent work on the peeling properties of heterogeneous adhesives.

And show you through this example how we can bridge microscopic properties of brittle systems with their macroscopic effective failure properties.

I started this work as a post-doc at Caltech with my colleauges . And I pursued it at Institut dAlembert in Paris where I am currently working as a CNRS researcher.

Some background explanations: post-doc at Caltech where you did this workThen, CNRS position when you pursued it.You are interested by the failure properties of heterogeneous solids, and you develop new approaches in order to integrate the effect of material microstructure on their macroscopic failure properties1s0s0Youngs modulus:Eeff average (Elocal)Fracture energy:Gceff average (Gclocal)XPredicting the effective toughness of heterogeneous systems:A challenging multi-scale problem2pour vous prsenter la position du problme, considrons un matriau fissur sous contrainte extrieure.s0s0Predicting the effective toughness of heterogeneous systems:A challenging multi-scale problems (r)rStress field diverges at the crack tips0s0Predicting the effective toughness of heterogeneous systems:A challenging multi-scale problems (r)rMacroscopic failure properties strongly dependent on material heterogeneitiesStress field diverges at the crack tips0s0Macroscopic failure properties strongly dependent on material heterogeneitiesOpens the door to microstructure design in order to achieve improved failure propertiesPredicting the effective toughness of heterogeneous systems:A challenging multi-scale problems (r)rStress field diverges at the crack tipApplication: Asymmetric adhesives

S. Xia, L. Ponson, G. Ravichandran and K. Bhattacharya, Phys. Rev. Lett. 2012 and International Patent 2011

Hard directionEasy direction6Goal: Developing a theoretical framework that predicts the effective resistance of heterogeneous brittle systems Using it for designing systems with improved failure properties1- Theoretical approach: Equation of motion for a crack in an heterogeneous materialFailure as a depinning transition2- Confrontation with experiments in the case of materials with disordered microstructuresEffective fracture energy of disordered materials3- Application to material design in the context of thin film adhesivesEnhancement and asymmetry of peeling strengthApproach & outline:7

What are the effects of heterogeneities on the propagation of a crack?zxGext1. Theory: deriving the equation of motion of a crack8coualitative

What are the effects of heterogeneities on the propagation of a crack?Pinning of the crack front:zxGext1. Theory: deriving the equation of motion of a crack9coualitative

Real material = GC(M) = + Gc(M)HomogeneousmaterialHypothesis:-Brittle material-Quasi-static crack propagationzxGexty1. Theory: deriving the equation of motion of a crackFracture energy fluctuations+10

Real material = GC(M) = + Gc(M)Fracture energy fluctuationsHomogeneousmaterial+Hypothesis:-Brittle material-Quasi-static crack propagationzxGexty1. Theory: deriving the equation of motion of a crackRandom quenched noise with amplitude Gc

For disordered materials11Elasticity of the material Crack front as an elastic line:

Real material = GC(M) = + Gc(M)Homogeneousmaterialzxf(z,t)My

GextJ. Rice (1985)1. Theory: deriving the equation of motion of a crackFracture energy fluctuations+12Elasticity of the material Crack front as an elastic line:

Real material = GC(M) = + Gc(M)Homogeneousmaterial

Equation of motion for a crack zxMyGext

L. B. Freund (1990)J. Rice (1985)1. Theory: deriving the equation of motion of a crackf(z,t)Fracture energy fluctuations+13Elasticity of the material Crack front as an elastic line:

Real material = GC(M) = + Gc(M)HomogeneousmaterialEquation of motion for a crack zxMyGext

J. Rice (1985)1. Theory: deriving the equation of motion of a crackJ. Schmittbuhl et al. 1995, D. Bonamy et al. 2008, L. Ponson et al. 2010f(z,t)

Fracture energy fluctuations+14Elasticity of the material Crack front as an elastic line:

Real material = GC(M) = + Gc(M)HomogeneousmaterialEquation of motion for a crack zxMyGext

J. Rice (1985)1. Theory: deriving the equation of motion of a crackCrack propagation as an elastic interface driven in a heterogeneous planef(z,t)J. Schmittbuhl et al. 1995, D. Bonamy et al. 2008, L. Ponson et al. 2010

Fracture energy fluctuations+15Predictions on the dynamics of cracksGextGextVariations of the average crack velocity with the external driving force

Vcrack

1. Theory: deriving the equation of motion of a crackFor disordered materials16Predictions on the dynamics of cracksGextGextVariations of the average crack velocity with the external driving force

StablePropagatingToughening effect

Effective fracture energy:Vcrack1. Theory: deriving the equation of motion of a crack17Predictions on the dynamics of cracksGextGextVariations of the average crack velocity with the external driving force

StablePropagatingToughening effect

Effective fracture energy:Power law variation of the crack velocityCrack velocity:

Vcrack

1. Theory: deriving the equation of motion of a crack18Predictions on the dynamics of cracksGextGextVariations of the average crack velocity with the external driving force

StablePropagatingToughening effect

Effective fracture energy:Power law variation of the crack velocityCrack velocity:

Fluctuations of velocityIntermittent dynamics of cracksPower law distributed fluctuations of velocityVcrack

1. Theory: deriving the equation of motion of a crack19

Variations of the average crack velocity with the external driving force2. Confrontation with experiments on disordered materialsConfrontation with experimental observationsFracture test of a disordered brittle rockL. Ponson, Phys. Rev. Lett. 2009

Variations of the average crack velocity with the external driving force2. Confrontation with experiments on disordered materialsConfrontation with experimental observationsFracture test of a disordered brittle rockL. Ponson, Phys. Rev. Lett. 2009Critical regime

Variations of the average crack velocity with the external driving forceL. Ponson, Phys. Rev. Lett. 20092. Confrontation with experiments on disordered materialsConfrontation with experimental observationsFracture test of a disordered brittle rockSubcritical regime(thermally activated)

Critical regime

Variations of crack velocity as a function of time

Fracture test of a disordered brittle rock2. Confrontation with experiments on disordered materialsConfrontation with experimental observations

Dfinition of the size S of a fluctuationFluctuations of velocity

L. Ponson, Phys. Rev. Lett. 2009Subcritical regime(thermally activated)

Critical regime

Variations of the average crack velocity with the external driving forceD. Bonamy, S. Santucci and L. Ponson, Phys. Rev. Lett. 2008

Variations of crack velocity as a function of time

Fracture test of a disordered brittle rock2. Confrontation with experiments on disordered materialsConfrontation with experimental observationsDfinition of the size S of a fluctuationFluctuations of velocity

L. Ponson, Phys. Rev. Lett. 2009Subcritical regime(thermally activated)

Critical regime

Variations of the average crack velocity with the external driving force

D. Bonamy, S. Santucci and L. Ponson, Phys. Rev. Lett. 2008

Variations of crack velocity as a function of time

Fracture test of a disordered brittle rock2. Confrontation with experiments on disordered materialsConfrontation with experimental observationsDfinition of the size S of a fluctuationFluctuations of velocity

L. Ponson, Phys. Rev. Lett. 2009Subcritical regime(thermally activated)

Critical regime

Variations of the average crack velocity with the external driving force

Distribution of fluctuation sizesExperimental results, Maloy, Santucci et al.Theoretical predictionsP(S) ~ S-with ~ 1.65D. Bonamy, S. Santucci and L. Ponson, Phys. Rev. Lett. 2008

Variations of crack velocity as a function of time

Fracture test of a disordered brittle rock2. Confrontation with experiments on disordered materialsConfrontation with experimental observationsDfinition of the size S of a fluctuationFluctuations of velocity

L. Ponson, Phys. Rev. Lett. 2009Subcritical regime(thermally activated)

Critical regime

Variations of the average crack velocity with the external driving forceD. Bonamy, S. Santucci and L. Ponson, Phys. Rev. Lett. 2008

Distribution of fluctuation sizesExperimental results, Maloy, Santucci et al.Theoretical predictionsP(S) ~ S-with ~ 1.65Failure of disordered brittle solids as a depinning transitionApplication: Effective fracture energy of disordered solids

Propagation direction2. Effective fracture energy of disordered materials

Equation of motion of the crackFracture energy randomly distributed with standard deviation Gc27Application: Effective fracture energy of disordered solids

Propagation direction2. Effective fracture energy of disordered materials

Equation of motion of the crackEffective fracture energy given by the depinning thresholdFracture energy randomly distributed with standard deviation Gc

Effect of disorder strength Gc? Of its distribution (Gaussian, bivalued)?z

282. Effective fracture energy of disordered materialsTheory: A simplified linear model inspired by Larkin

Propagation direction

A. Larkin and Y. Ovchinnikov (1979)292. Effective fracture energy of disordered materialsTheory: A simplified linear model inspired by Larkin

Validity range: so that

Propagation direction

A. Larkin and Y. Ovchinnikov (1979)Front geometryLarkin length

zz302. Effective fracture energy of disordered materialsTheory: A simplified linear model inspired by Larkin

Validity range: so that

Typical resistance felt by a domain of size L if L