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Institute for Mechanics of Materials and Structures Vienna University of Technology Micromechanical model for the description of fatigue behavior of asphalt mixtures 18th Inter-Institute Seminar for Young Researchers September 2011, Budapest Josef FÜSSL 1 and Roman LACKNER 2 1 Institute for Mechanics of Materials and Structures (IMWS), TU Wien 2 Material-Technology Innsbruck (MTI), University of Innsbruck

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Institute for Mechanics of Materials and Structures Vienna University of Technology crack-network due to fatigue continuous traffic loading wearing course base layer Fatigue – Motivation

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Institute for Mechanics of Materials and Structures Vienna University of Technology The following processes are taking place: initiation and propagation of microcrack-network development of macrocracks parasitic effects: self-heating, binder-thixotropy, … initiation and propagation of microcracks development of macrocracks failure complex modulus load cycles Physical mechanisms

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Institute for Mechanics of Materials and Structures Vienna University of Technology Experimental observations DTC 4-PBB strain-controlled stress- controlled... dynamic stiffness modulus... phase angle... number of load cycles decreases with increases with

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Institute for Mechanics of Materials and Structures Vienna University of Technology Phenomenological approach: Relationships between initial stress or strain and number of load repetitions to „failure“: simple to use does not account for how damage evolves only valid for a given set of test (loading) conditions … number of repetitions to failure … magnitude of tensile strain repeatedly applied … initial mixture stiffness … experimentally determined coefficients Fatigue models

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Institute for Mechanics of Materials and Structures Vienna University of Technology Micromechanics: Multiscale model Fracture mechanics: Crack growth criterion new micromechanics-based fatigue model fatigue performance as a function of composition (mix design), morphology, and the properties of the material phases (e.g., bitumen, filler,...) applicable to different loading conditions Fatigue models

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Institute for Mechanics of Materials and Structures Vienna University of Technology Implementation in Multiscale Model consideration of microcracks at mortar-scale

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Institute for Mechanics of Materials and Structures Vienna University of Technology INPUT: crack density d mix-design (volume fractions) elastic properties of sand viscoelastic properties of mastic Mortar-scale Asphalt-scale Macroscale viscoelastic homogenization … crack density INPUT: mix-design (volume fractions) elastic properties of stone OUTPUT: Implementation in Multiscale Model

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Institute for Mechanics of Materials and Structures Vienna University of Technology Determination of crack density inserting integration numerical solution via linear approximation of... crack radius... number of cracks... generalized -integral... “dissipated pseudo strain energy” Interrelation between fracture mechanics and continuum micromechanics Paris crack growth criterion for viscoelastic materials [Schapery 1984] definition of crack density within micromechanics

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Institute for Mechanics of Materials and Structures Vienna University of Technology... constant parameter for a specific mastic material, depending on the tensile strength and the bond energy of the mastic Determination of crack density numerical solution of differential equation... determined from relaxation modulus... dimensionless parameter... dynamic modulus of mastic... initial dynamic modulus of asphalt... stress amplitude... number of load cycles determined through solution of diff. equation inserting

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Institute for Mechanics of Materials and Structures Vienna University of Technology Ermüdungsmodell Experimente Asphalt: PmB bei -10 C, = 30 Hz, = 1.084/1.301/1.518 MPa Results – comparison to experimental data

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Institute for Mechanics of Materials and Structures Vienna University of Technology fatigue model experiments asphalt: B50-70 at 0 C, = 30 Hz, = 0.475/0.633/0.791 MPa Results – comparison to experimental data

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Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of shear modulus of aggregates on fatigue performance of asphalt increasing shear modulus increasing crack density

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Institute for Mechanics of Materials and Structures Vienna University of Technology Influence of sand content on fatigue performance of asphalt increasing sand content increasing crack density Sensitivity Study

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Institute for Mechanics of Materials and Structures Vienna University of Technology Influence of frequency on fatigue performance of asphalt increasing frequency increasing crack density Sensitivity Study

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Institute for Mechanics of Materials and Structures Vienna University of Technology Conclusions Fatigue model gives insights into the sensitivity of fatigue performance of asphalt with respect to the mix design Experimentally observed characteristics of dynamic stiffness modulus and phase angle are correctly reproduced by the proposed fatigue model Combining fracture mechanics and micromechanics allows us to relate all experimental oberserved phenomena to physical quantities and processes

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Institute for Mechanics of Materials and Structures Vienna University of Technology TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA Thank you for your attention

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Institute for Mechanics of Materials and Structures Vienna University of Technology Results – comparison to experimental data Homogenization from mortar-scale to macroscale (asphalt)

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Institute for Mechanics of Materials and Structures Vienna University of Technology Asphalt: B50-70 bei -10 C, = 10/30 Hz, = 0.912/1.277/1.459 MPa Results – comparison to experimental data fatigue model experiments

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Institute for Mechanics of Materials and Structures Vienna University of Technology Implementation in Multiscale Model consideration of microcracks at mortar-scale

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Institute for Mechanics of Materials and Structures Vienna University of Technology Phenomenological approach: Relationships between initial stress or strain and number of load repetitions to „failure“: simple to use does not account for how damage evolves only valid for a given set of test (loading) conditions … number of repetitions to failure … magnitude of tensile strain repeatedly applied … initial mixture stiffness … experimentally determined coefficients Fatigue models

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Institute for Mechanics of Materials and Structures Vienna University of Technology Mechanistic approach: Use of damage mechanics or fracture mechanics with or without viscoelasticity. more complex approach provide relationships between material properties and fatigue performance applicable to broader range of loading and environmental conditions Continuum damage mechanics Fracture mechanics … internal state variable … damage evolution rate … thermodynamic force … positive constant … crack length … generalized -integral … positive constant Continuum micromechanics: multiscale model New approach -integral: work (energy) per unit fracture surface area [Jim Rice 1968] Fatigue models

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Institute for Mechanics of Materials and Structures Vienna University of Technology Viscoelastic homogenization using continuum micromechanics The introduction of microcracks in the Mori-Tanaka scheme leads to the following expression for the homogenized material tensor: … additional terms for consideration of microcracks … material tensor (stiffness of material) … crack density … localization tensor for randomized crack distribution … volume fractions of different material phases … Eshelby tensor (material morphology) … material tensor (stiffness of matrix)

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Institute for Mechanics of Materials and Structures Vienna University of Technology Influence of stone content on fatigue performance of asphalt increasing stone content increasing crack density Sensitivity Study

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Institute for Mechanics of Materials and Structures Vienna University of Technology Influence of air-void content on fatigue performance of asphalt increasing air-void content increasing crack density Sensitivity Study

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Institute for Mechanics of Materials and Structures Vienna University of Technology Influence of stress amplitude on fatigue performance of asphalt increasing stress amplitude increasing crack density Sensitivity Study

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Institute for Mechanics of Materials and Structures Vienna University of Technology Bestimmung der Rissdichte numerische Lösung der Differentialgleichung

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Institute for Mechanics of Materials and Structures Vienna University of Technology Ergebnisse – Mastixeigenschaften Ermüdung unabhängig von Frequenz und Amplitude

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Institute for Mechanics of Materials and Structures Vienna University of Technology DSR – Identifizierung der Mastixeigenschaften Materialparameter für Mastix: INPUT Mehrskalenmodell

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Institute for Mechanics of Materials and Structures Vienna University of Technology Viscoelastic energy dissipation + damage Viscoelastic energy dissipation only Damage (cracking and plastic deformations) Elastically stored energy … apparent phase angle … viscoelastic phase angle Determination of Generalized J-Integral

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Institute for Mechanics of Materials and Structures Vienna University of Technology Composition of asphalt Bitumen (binder) Aggregate:filler(Ø ≤ 125 mm) sand(Ø ≤ 2 mm) stone(Ø > 2 mm) Air voids Types of asphalt Gussasphalt (air voids f a = 0) Asphalt concrete (3% < f a < 5%) Stone-mastic asphalt (f a < 7%) Porous asphalt (12% < f a < 17%) Modes of optimization Change of mix design Selection of appropriate constituents Change of properties of constituents (e.g.: polymer-modified bitumen) Large variability in asphalt composition Characteristics of Asphalt

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Institute for Mechanics of Materials and Structures Vienna University of Technology Realistic assessment and prediction of durability of flexible pavements is still missing Failure in flexible pavements: service life from -30 °C < T < 70 °C Motivation Increasing commercial traffic Recent developments regarding truck tires: from dual tires to single tires -> Increase of contact stresses Low-temperature cracking T < -10°C Fatigue T < 30°C Rutting T > 30°C

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Institute for Mechanics of Materials and Structures Vienna University of Technology Motivation thermisch induzierte Rissbildung T < -10°C Ermüdung T < 30°C Spurrinnenbildung T > 30°C Schadensbilder bei flexiblen Straßenbefestigungen Beschreibung des Materialverhaltens: Heute:mittels empirischen makroskopischen Modellen Zukunft: mittels Modellen basierend auf der Mikromechanik Ziel: realistische Vorhersage des Verhaltens von flexiblen Straßenbefestigungen + ansteigendes Verkehrsaufkommen + ansteigende Kontaktspannungen zwischen Reifen und Straße

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Institute for Mechanics of Materials and Structures Vienna University of Technology elastische Eigenschaften analytische Methoden (Kontinuumsmikromechanik) Mori-Tanaka/Selbstkonsistenz Schema Homogenisierung von Mehrphasenwerkstoffen Materialphasen: Matrix Aggregate Grenzflächen Hohlräume (Poren) Ablöseeffekte Mikrorisse Homogenisierungsverfahren viskoelastische Eigenschaften analytische Methoden (KMM) correspondence principle („Laplace-Carson“ Raum) Festigkeitseigenschaften analytische Methoden Finite-Elemente Methode numerische Traglastanalyse Schädigung (Ermüdung) empirische Ansätze Schädigungs- und Bruchmechanik KMM + Bruchmechanik ~ ? ~ ~

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Institute for Mechanics of Materials and Structures Vienna University of Technology –Identification of mechanical properties on each scale –Upscaling of elastic (aggregate), viscoelastic (bitumen), and fatigue properties Introduction of five scales of observation Scales of observation: Multiscale Model for Asphalt

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