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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 Josef FÜSSL1 and Roman LACKNER2 1Institute for Mechanics of Materials and Structures (IMWS), TU Wien 2Material-Technology Innsbruck (MTI), University of Innsbruck 18th Inter-Institute Seminar for Young Researchers 23.-25. September 2011, Budapest Institute for Mechanics of Materials and Structures Vienna University of Technology Fatigue – Motivation crack-network due to fatigue continuous traffic loading wearing course base layer Institute for Mechanics of Materials and Structures Vienna University of Technology Physical mechanisms complex modulus initiation and propagation of microcracks development of macrocracks failure load cycles The following processes are taking place: initiation and propagation of microcrack-network development of macrocracks parasitic effects: self-heating, binder-thixotropy, … Institute for Mechanics of Materials and Structures Vienna University of Technology Experimental observations 4-PBB strain-controlled DTC stresscontrolled ... dynamic stiffness modulus ... phase angle ... number of load cycles decreases with increases with Institute for Mechanics of Materials and Structures Vienna University of Technology Fatigue models Phenomenological approach: Relationships between initial stress or strain and number of load repetitions to „failure“: … number of repetitions to failure … magnitude of tensile strain repeatedly applied … initial mixture stiffness … experimentally determined coefficients simple to use does not account for how damage evolves only valid for a given set of test (loading) conditions Institute for Mechanics of Materials and Structures Vienna University of Technology Fatigue models 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 Institute for Mechanics of Materials and Structures Vienna University of Technology Implementation in Multiscale Model consideration of microcracks at mortar-scale Institute for Mechanics of Materials and Structures Vienna University of Technology Implementation in Multiscale Model Mortar-scale Asphalt-scale INPUT: mix-design (volume fractions) elastic properties of stone Macroscale OUTPUT: viscoelastic homogenization INPUT: crack density d mix-design (volume fractions) elastic properties of sand viscoelastic properties of mastic Institute for Mechanics of Materials and Structures Vienna University of Technology Determination of crack density Interrelation between fracture mechanics and continuum micromechanics Paris crack growth criterion for viscoelastic materials [Schapery 1984] definition of crack density within micromechanics inserting integration numerical solution via linear approximation of ... crack radius ... number of cracks ... generalized -integral ... “dissipated pseudo strain energy” Institute for Mechanics of Materials and Structures Vienna University of Technology Determination of crack density numerical solution of differential equation ... constant parameter for a specific mastic material, depending on the tensile strength inserting and the bond energy of the mastic ... dimensionless parameter ... determined from relaxation modulus ... dynamic modulus of mastic ... initial dynamic modulus of asphalt ... stress amplitude ... number of load cycles Institute for Mechanics of Materials and Structures Vienna University of Technology Results – comparison to experimental data Asphalt: PmB45-80-65 bei -10 C, = 30 Hz, = 1.084/1.301/1.518 MPa Ermüdungsmodell Experimente Institute for Mechanics of Materials and Structures Vienna University of Technology Results – comparison to experimental data asphalt: B50-70 at 0 C, = 30 Hz, = 0.475/0.633/0.791 MPa fatigue model experiments 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 crack density increasing shear modulus Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of sand content on fatigue performance of asphalt increasing crack density increasing sand content Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of frequency on fatigue performance of asphalt increasing crack density increasing frequency 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 Institute for Mechanics of Materials and Structures Vienna University of Technology Thank you for your attention Institute for Mechanics of Materials and Structures Vienna University of Technology Results – comparison to experimental data Homogenization from mortar-scale to macroscale (asphalt) Institute for Mechanics of Materials and Structures Vienna University of Technology Results – comparison to experimental data Asphalt: B50-70 bei -10 C, = 10/30 Hz, = 0.912/1.277/1.459 MPa fatigue model experiments Institute for Mechanics of Materials and Structures Vienna University of Technology Implementation in Multiscale Model consideration of microcracks at mortar-scale Institute for Mechanics of Materials and Structures Vienna University of Technology Fatigue models Phenomenological approach: Relationships between initial stress or strain and number of load repetitions to „failure“: … number of repetitions to failure … magnitude of tensile strain repeatedly applied … initial mixture stiffness … experimentally determined coefficients simple to use does not account for how damage evolves only valid for a given set of test (loading) conditions Institute for Mechanics of Materials and Structures Vienna University of Technology Fatigue models Mechanistic approach: Use of damage mechanics or fracture mechanics with or without viscoelasticity. New approach Continuum damage mechanics … … … … internal state variable damage evolution rate thermodynamic force positive constant Fracture mechanics … crack length … generalized -integral … positive constant Continuum micromechanics: multiscale model more complex approach provide relationships between material properties and fatigue performance applicable to broader range of loading and environmental conditions -integral: work (energy) per unit fracture surface area [Jim Rice 1968] 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 … crack density … localization tensor for randomized crack distribution … material tensor (stiffness of material) … material tensor (stiffness of matrix) … Eshelby tensor (material morphology) … volume fractions of different material phases Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of stone content on fatigue performance of asphalt increasing crack density increasing stone content Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of air-void content on fatigue performance of asphalt increasing crack density increasing air-void content Institute for Mechanics of Materials and Structures Vienna University of Technology Sensitivity Study Influence of stress amplitude on fatigue performance of asphalt increasing crack density increasing stress amplitude Institute for Mechanics of Materials and Structures Vienna University of Technology Bestimmung der Rissdichte numerische Lösung der Differentialgleichung Institute for Mechanics of Materials and Structures Vienna University of Technology Ergebnisse – Mastixeigenschaften Ermüdung unabhängig von Frequenz und Amplitude Institute for Mechanics of Materials and Structures Vienna University of Technology DSR – Identifizierung der Mastixeigenschaften Materialparameter für Mastix: INPUT Mehrskalenmodell Institute for Mechanics of Materials and Structures Vienna University of Technology Determination of Generalized J-Integral Elastically stored energy … apparent phase angle … viscoelastic phase angle Viscoelastic energy dissipation + damage Viscoelastic energy dissipation only Damage (cracking and plastic deformations) Institute for Mechanics of Materials and Structures Vienna University of Technology Characteristics of Asphalt Large variability in asphalt composition Composition of asphalt Bitumen (binder) Aggregate: filler sand stone Air voids (Ø ≤ 125 mm) (Ø ≤ 2 mm) (Ø > 2 mm) Types of asphalt Gussasphalt (air voids fa = 0) Asphalt concrete (3% < fa < 5%) Stone-mastic asphalt (fa < 7%) Porous asphalt (12% < fa < 17%) Modes of optimization Change of mix design Selection of appropriate constituents Change of properties of constituents (e.g.: polymer-modified bitumen) Institute for Mechanics of Materials and Structures Vienna University of Technology Motivation • Increasing commercial traffic • Recent developments regarding truck tires: from dual tires to single tires -> Increase of contact stresses • Failure in flexible pavements: service life from -30 °C < T < 70 °C Low-temperature cracking T < -10°C Fatigue T < 30°C Rutting T > 30°C Realistic assessment and prediction of durability of flexible pavements is still missing Institute for Mechanics of Materials and Structures Vienna University of Technology Motivation Schadensbilder bei flexiblen Straßenbefestigungen + ansteigendes Verkehrsaufkommen + ansteigende Kontaktspannungen zwischen Reifen und Straße thermisch induzierte Rissbildung T < -10°C Ermüdung T < 30°C Spurrinnenbildung T > 30°C Beschreibung des Materialverhaltens: Heute: mittels empirischen makroskopischen Modellen Zukunft: mittels Modellen basierend auf der Mikromechanik Ziel: realistische Vorhersage des Verhaltens von flexiblen Straßenbefestigungen Institute for Mechanics of Materials and Structures Vienna University of Technology Homogenisierung von Mehrphasenwerkstoffen Materialphasen: Matrix Aggregate Grenzflächen Hohlräume (Poren) Mikrorisse Ablöseeffekte Homogenisierungsverfahren elastische Eigenschaften analytische Methoden (Kontinuumsmikromechanik) Mori-Tanaka/Selbstkonsistenz Schema 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 ? ~ ~ ~ Institute for Mechanics of Materials and Structures Vienna University of Technology Multiscale Model for Asphalt Scales of observation: Introduction of five scales of observation – Identification of mechanical properties on each scale – Upscaling of elastic (aggregate), viscoelastic (bitumen), and fatigue properties