Models for Plastic Deformation Based on Non-Linear Response for FEM Implementation Eyad Masad Zachry Department of Civil Engineering Texas A&M University, College Station, TX International Workshop on Asphalt Binders and Mastics Madison, Wisconsin. September 16-17 Acknowledge Funding by Asphalt Research Consortium
Outline Motivation Viscoelastic-Viscoplastic-Viscodamage Models Identification of model parameters and model validation Implementation procedure Application of the model for rutting performance simulation Conclusions and future works
Motivation Prediction of pavement performance Material Characteristics Aggregate shape Anisotropy Adhesive and Cohesive bond strengths Healing Binder rheology Pavement Structure Environmental Factors Thickness Temperature Sub grade type Humidity differential Rainfall FEM Modeling Loading Conditions Type of loading Tire pavement interaction Calibration (minimize shift factor dependency) Prediction of material distress
Mechanical Response of Asphalt Mixes Thermo-Chemo-Hygro-Mechanical Viscoelastic-Viscoplastic-Viscodamage Constitutive Model Percent of Strain VE VP Strain Temperature Increase and/or decrease in strain rate Strain Time Time Viscoelastic Viscoplastic
Mechanical Response of Asphalt Mixes Thermo-Chemo-Hygro-Mechanical Viscoelastic-Viscoplastic-Viscodamage Constitutive Model Rate- and Time-dependent softening 10000 Stress 5 7500 4 5000 Axial strain (%) 3 2 2500 1 0 0 2 4 6 8 10 12 14 Strain 0 0 200 400 600 800 1000 1200 Time (Sec) Displacement control tests Repeated creep-recovery test
Outline Viscoelastic-Viscoplastic-Viscodamage Models
Viscoelastic Properties Thermo-Chemo-Hygro-Mechanical Nonlinear Viscoelastic Model (Schapery, Constitutive 1969) Model ve t d 0 0 1 2 d 0 gd g D gd Nonlinear contribution in the elastic response, due to the level of stress Nonlinear contribution in the transient response Nonlinear contribution in the viscoelastic response due to the level of stress dt a t 0 T N n1 D Dn 1exp nt Temperature shift factor Prony series coefficients Retardation time
Viscoplastic Model (Perzyna, 1971) ve vp ij ij ij Viscoplastic Properties Perzyna Model vp vp f F I Yield surface ij e 1 e (Extended Drucker-Prager) vp 0 1 1exp 2 e Hardening function Flow Rule: vp ij vp T f N g ij f Viscoplastic f 0 Plastic potential function: Overstress function g I 1 f 0 f 0 f f 0 Viscoelastic Yield surface
Extended Drucker-Prager Yield Surface Accounts for: Dilation and confinement pressure The effect of shear stress Work hardening of the material Yield surface f I 1 vp g I 1 Potential function I 1
Viscoplastic Properties Effect of parameter d on the yield surface Influence of stress path on the yielding point J 1 1 1 1 2 J 2 3 3/2 d d J2
Strength Degradation due to Damage T 1 T T Damaged Configuration A Remove Both Voids and Cracks A A A 0 1 T A Effective Undamaged Configuration Nominal (measured) stress 0 No damage Effective stress 1 Failure Damage density 0 1 Damage
Viscodamage Model Viscodamage model (Darabi, Abu Al-Rub, Masad, Little; 2010) q 2 vd Y 1 exp Tot T k exp 1 Y 0 T 0 Y J 1 1 J 1 1 I 3/2 2 d d J 2 Damage force 2 3 1 Damage response is different in compression or extension Damage is sensitive to Loading Mode Damage is sensitive to hydrostatic pressure I 1 : First stress invariant J 2 and J 3 : The second and the third deviatoric stress invariants
Determination of Model Parameters Creep-Recovery test @ reference temperature Recovery part of the Creep- Recovery test @ reference temperature Creep part of the Creep- Recovery test @ reference temperature Two creep tests that show tertiary behavior @ reference temperature Creep test in tension @ reference temperature Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains. Determination of viscoelastic parameters @ reference temperature Determination of viscoplastic parameters @ reference temperature Determination of viscodamage parameters @ reference temperature Determination of d parameters Creep-recovery and creep tests @ other temperatures Determination temperature-dependent model parameters
Determination of Model Parameters Creep-Recovery test @ reference temperature Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains. vp t g D g g Dt t a 0 0 1 2 a a Stress vp t gg DtDtt t 1 2 a During the recovery: vp vp t t a Strain t a Time t t a 0 0 1 2 a Dt Dt t gdgg Dt a t a t t a Time Pure viscoelastic response. Can be used for identifying VE parameters
Creep part of the Creep- Recovery test @ reference temperature Determination of Model Parameters Determination of viscoplastic parameters @ reference temperature Strain Total strain (experimental measurements) Viscoelastic response. Model predictions using the Identified VE model parameters. t a Time Viscoplastic response. Obtained by subtracting the VE response from the experimental measurements Pure viscoplastic response. Can be used for identifying VP parameters
Determination of Model Parameters A creep tests that show tertiary behavior @ reference temperature and stress level Strain Determination of viscodamage parameters @ reference temperature Total strain (experimental measurements) @ reference temperature and stress level Deviation from the experimental data at tertiary stage due to damage Model response using identified VE-VP model parameters Time @ reference temperature T=T 0 exp 1 T T 1 0 @ reference stress Y=Y 0 vd 2 Tot 1 exp k Identify these damage parameters Using the creep test at reference temperature and stress level
Determination of Model Parameters Another creep tests that show tertiary behavior @ reference temperature and other stress level Strain Determination of viscodamage parameters @ reference temperature Total strain (experimental measurements) @ reference temperature and stress level Deviation from the time of failure due to stress dependency parameter q Model response using identified VE-VP-VD model parameters @ reference temperature T=T 0 exp 1 T T 1 0 Time q vd Y Y 0 2 Tot 1 exp k Identify the stress dependency parameter q Known
Stress Levels within the Pavements Gibson et al., 2010
Model Validation Tests Test Temperature ( o C) Stress Level (kpa) Loading time (Sec) Strain Rate (1/Sec) 10 2000, 2500 300, 350, 400 Creep-Recovery 20 1000, 1500 30, 40, 130, 210 40 500, 750 35, 130, 180 10 2000, 2500 Compression Creep 20 1000, 1500 40 500, 750 Tension Constant strain rate test Creep Constant strain rate test 10 0.005, 0.005, 0.00005 20 0.005, 0.005, 0.00005 40 0.005, 0.005 10 500, 1000, 1500 20 500, 700 35 100, 150 20 0.0167, 0.00167
Outline Model Validation
Model Validation (Creep-Recovery Test) 1- Model can predict creep-recovery data at different temperatures and stress levels. (Compression) o T 10 C 2000kPa o T 10 C 2500kPa Creep-recovery test Compression @ T=10 o C
Model Validation (Creep-Recovery Test) 1- Model can predict creep-recovery data at different temperatures and stress levels. (Compression) o T 20 C 1000kPa o T 20 C 1500kPa Creep-recovery test Compression @ T=20 o C
Model Validation (Creep-Recovery Test) 1- Model can predict creep-recovery data at different temperatures and stress levels. (Compression) o T 40 C 500kPa o T 40 C 750kPa Creep-recovery test Compression @ T=40 o C
Model Validation (Creep Test) 2-Model predictions agrees well with creep data at different temperatures and stress levels. Tertiary creep behavior is also captured. T 10 o C T 20 o C Creep test Compression
Model Validation (Creep Test) 2-Model predictions agrees well with creep data at different temperatures and stress levels. Tertiary creep behavior is also captured. T 40 o C Creep test Compression
Model Validation (Constant Strain Rate Test) 3-Model predicts temperature and rate-dependent behavior of asphalt mixes. Post peak behavior is captured well. 1 T=10 0.9 0.8 T=20 Damage density 0.7 0.6 0.5 0.4 T=40 0.3 0.2 0.1 0 0 2 4 6 8 10 12 Strain (%) T=10 T=20 T=40 Constant strain rate test Compression Loading rate: 0.005/Sec
Model Validation (Constant Strain Rate Test) 3-Model predicts temperature and rate-dependent behavior of asphalt mixes. Post peak behavior is captured well. 3000 T=10 T=10 2500 2000 T=10 T=20 T=20 Stress (kpa) 1500 1000 T=20 T=40 T=40 500 0 0 2 4 6 8 10 12 14 Strain (%) Constant strain rate test Compression Loading rate: 0.0005/Sec Constant strain rate test Compression Loading rate: 0.00005/Sec
Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well. 2.5 1500 kpa 2.5 700 kpa 500 kpa 2.0 2.0 300 kpa Axial strain (%) 1.5 1.0 1000 kpa 500 kpa Axial strain (%) 1.5 1.0 0.5 Experimental data Model prediction 0.5 Experimental data Model prediction 0.0 0 300 600 900 1200 1500 Time (Sec) 0.0 0 100 200 300 400 500 Time (Sec) Creep test Tension Temperature: 10 o C Creep test Tension Temperature: 20 o C
Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well. 2.5 2.0 150 kpa Creep test Tension Temperature: 35 o C Axial strain (%) 1.5 1.0 100 kpa 0.5 0.0 Experimental data Model prediction 0 50 100 150 200 Time (Sec)
Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension. 5000 1 4000 0.0167 / Sec 0.9 0.8 0.7 Stress (kpa) 3000 2000 1000 0.00167 / Sec Damage density 0.6 0.5 0.4 0.3 0.2 Strain rate=0.0167/sec Strain rate=0.00167/sec 0.1 0 0 2 4 6 8 10 12 Strain (%) 0 0 2 4 6 8 10 12 Strain (%) Constant strain rate test Tension Temperature: 20 o C
Outline Implementation procedure
Implementation Procedure Procedure to Run the Performance Prediction Continuum Damage Model Fortran Fortran compiler is used to compile UMAT (i.e. translates programming commands into action). UMAT A Fortran code includes the Continuum Damage Model Abaqus interface Abaqus calls UMAT to run the Continuum Damage Model and UMAT gives Abaqus the material response Pavement Section Loaded region Mesh Boundary Conditions Creating geometry, mesh, and applying loading Simulating Rutting Running and viewing the simulation results
Outline Application of the model for rutting performance simulation
Application for Simulation of Wheel Tracking Test 2D FE Model 3D FE Model
Application: Different Loading Cases Mode Loading approach Loading Area Schematic representation of loading modes 1 (2D) Pulse loading (plane strain) One wheel 2 (2D) Equivalent loading (plane strain) One wheel 3 (2D) Pulse loading (axisymmetric) One wheel 4 (2D) Equivalent loading (axisymmetric) One wheel 5 (3D) Pulse loading One wheel 6 (3D) Equivalent loading One wheel 7 (3D) Pulse loading Whole wheel path 8 (3D) Equivalent loading Whole wheel path 9 (3D) Pulse loading Circular loading area 10 (3D) Equivalent loading Circular loading area 11 (3D) Moving loading One wheel Moving Direction
Application: Different Loading Modes and Constitutive Models 0.12 0.1 Elastic-Viscoplastic Constitutive Model 2D Rutting simulation results: Different constitutive models. Rutting (mm) 0.08 0.06 0.04 Loading Mode 1 Loading Mode 2 Loading Mode 3 Loading Mode 4 0.02 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 0 0 200 400 600 800 1000 Cycles (N) 0.12 0.1 Viscoelastic-Viscoplastic Constitutive Model 0.16 0.14 0.12 Viscoelastic-Viscoplastic- Viscodamage Model Rutting (mm) 0.08 0.06 0.04 Loading Mode 1 Loading Mode 2 Rutting (mm) 0.1 0.08 0.06 0.02 Loading Mode 3 Loading Mode 4 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 0 0 200 400 600 800 1000 Cycles (N) 0.04 0.02 Loading Mode 1 Loading Mode 2 Loading Mode 3 Loading Mode 4 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 0 0 200 400 600 800 1000 Cycles (N)
Application: Different Loading Modes and Constitutive Models 3D Rutting simulation results: Different constitutive models. Rutting (mm) 0.14 0.12 0.1 0.08 0.06 Loading Mode 5 Loading Mode 6 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 Loading Mode 11 Elastic-Viscoplastic Constitutive Model 0.04 0.02 0 0 200 400 Cycles (N) 600 800 1000 0.14 0.12 0.1 Loading Mode 5 Loading Mode 6 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 Loading Mode 11 Viscoelastic-Viscoplastic Constitutive Model 0.14 0.12 0.1 Loading Mode 5 Loading Mode 6 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 Loading Mode 11 Rutting (mm) 0.08 0.06 Rutting (mm) 0.08 0.06 0.04 0.04 0.02 0 0 200 400 Cycles (N) 600 800 1000 0.02 Viscoelastic-Viscoplastic- Viscodamage Model 0 0 200 400 600 800 1000 Cycles (N)
Application: Different Loading Modes and Constitutive Models Simplified loading assumptions can be used when using elasto-viscoplastic model. Simplified loading assumptions should be used carefully when viscoelastic response is significant. Using simplified loading assumptions causes significant error when the damage level is significant.
Simulation Results Viscoplastic strain 2D Results 3D Results
Simulation Results Damage evolution 2D Results 3D Results
Compare with Experimental Data Rutting (mm) 14 12 10 8 6 4 2 0 Experimental Measurements 2D results 3D results 0 20000 40000 60000 80000 100000 120000 Cycles (N)
Applied stress (T=55 o C) ALF Data-Variable Stress Deviatoric stress (kpa) Time (Sec)
Model Validation: ALF Data (Strain Response) 1 st Cycle 2 nd Cycle 3 rd Cycle 4 th Cycle
Model Validation: ALF Data (Strain Response) 5 th Cycle 6 th Cycle 7 th Cycle 8 th Cycle
Model Validation: ALF Data (Strain Response) Model predictions at large loading cycles 4.50E 03 4.00E 03 exp cal. Total Strain 3.50E 03 3.00E 03 2.50E 03 2.00E 03 Deviatoric stress: 712kPa 1.50E 03 3004 3006 3008 3010 3012 3014 3016 Time (Sec) At large loading cycles model predictions using VE-VP deviates from experimental measurements This deviation is due to damage and should be compensated using the damage model.
Model Validation: ALF Data (Strain Response) Constant Stress-Variable Time Loading 0.035 0.03 Viscoplastic VP strain Strain 0.025 0.02 0.015 0.01 model exp 0.005 0 0 10 20 30 40 50 60 Cycle
Conclusions and Future Works Conclusions: Proposed viscoelastic-viscoplastic-viscodamage model predicts rate-, time-, and temperature-dependent behavior of asphalt mixes in both tension and compression. Model can be used to predict performance simulations. Challenges and future works: Including healing to the model. Including environmental effects such as aging and moisture induced damage to the model. Validating the model over an extensive experimental measurements. Performing performance simulations in pavements.
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