Eyad Masad Zachry Department of Civil Engineering Texas A&M University, College Station, TX

Transcription

1 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 Acknowledge Funding by Asphalt Research Consortium

2 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

3 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

4 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

5 Mechanical Response of Asphalt Mixes Thermo-Chemo-Hygro-Mechanical Viscoelastic-Viscoplastic-Viscodamage Constitutive Model Rate- and Time-dependent softening Stress Axial strain (%) Strain Time (Sec) Displacement control tests Repeated creep-recovery test

6 Outline Viscoelastic-Viscoplastic-Viscodamage Models

7 Viscoelastic Properties Thermo-Chemo-Hygro-Mechanical Nonlinear Viscoelastic Model (Schapery, Constitutive 1969) Model ve t d 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

8 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

9 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

10 Viscoplastic Properties Effect of parameter d on the yield surface Influence of stress path on the yielding point J J 2 3 3/2 d d J2

11 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

12 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 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

13 Determination of Model Parameters Creep-Recovery reference temperature Recovery part of the Creep- Recovery reference temperature Creep part of the Creep- Recovery reference temperature Two creep tests that show tertiary reference temperature Creep test in reference temperature Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains. Determination of viscoelastic reference temperature Determination of viscoplastic reference temperature Determination of viscodamage reference temperature Determination of d parameters Creep-recovery and creep other temperatures Determination temperature-dependent model parameters

14 Determination of Model Parameters Creep-Recovery reference temperature Separate viscoelastic (recoverable) and viscoplastic (irrecoverable) strains. vp t g D g g Dt t a 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 a Dt Dt t gdgg Dt a t a t t a Time Pure viscoelastic response. Can be used for identifying VE parameters

15 Creep part of the Creep- Recovery reference temperature Determination of Model Parameters Determination of viscoplastic 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

16 Determination of Model Parameters A creep tests that show tertiary reference temperature and stress level Strain Determination of viscodamage reference temperature Total strain (experimental reference temperature and stress level Deviation from the experimental data at tertiary stage due to damage Model response using identified VE-VP model parameters reference temperature T=T 0 exp 1 T T 1 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

17 Determination of Model Parameters Another creep tests that show tertiary reference temperature and other stress level Strain Determination of viscodamage reference temperature Total strain (experimental 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 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

18 Stress Levels within the Pavements Gibson et al., 2010

19 Model Validation Tests Test Temperature ( o C) Stress Level (kpa) Loading time (Sec) Strain Rate (1/Sec) , , 350, 400 Creep-Recovery , , 40, 130, , , 130, , 2500 Compression Creep , , 750 Tension Constant strain rate test Creep Constant strain rate test , 0.005, , 0.005, , , 1000, , , ,

20 Outline Model Validation

21 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 T=10 o C

22 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 T=20 o C

23 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 T=40 o C

24 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

25 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

26 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= T=20 Damage density T= Strain (%) T=10 T=20 T=40 Constant strain rate test Compression Loading rate: 0.005/Sec

27 Model Validation (Constant Strain Rate Test) 3-Model predicts temperature and rate-dependent behavior of asphalt mixes. Post peak behavior is captured well T=10 T= T=10 T=20 T=20 Stress (kpa) T=20 T=40 T= Strain (%) Constant strain rate test Compression Loading rate: /Sec Constant strain rate test Compression Loading rate: /Sec

28 Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well kpa kpa 500 kpa kpa Axial strain (%) kpa 500 kpa Axial strain (%) Experimental data Model prediction 0.5 Experimental data Model prediction Time (Sec) Time (Sec) Creep test Tension Temperature: 10 o C Creep test Tension Temperature: 20 o C

29 Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension. Tertiary stage and time of failure are captured well kpa Creep test Tension Temperature: 35 o C Axial strain (%) kpa Experimental data Model prediction Time (Sec)

30 Model Validation in Tension (Creep Test) 4-Model predicts experimental data in tension / Sec Stress (kpa) / Sec Damage density Strain rate=0.0167/sec Strain rate= /sec Strain (%) Strain (%) Constant strain rate test Tension Temperature: 20 o C

31 Outline Implementation procedure

32 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

33 Outline Application of the model for rutting performance simulation

34 Application for Simulation of Wheel Tracking Test 2D FE Model 3D FE Model

35 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

36 Application: Different Loading Modes and Constitutive Models Elastic-Viscoplastic Constitutive Model 2D Rutting simulation results: Different constitutive models. Rutting (mm) Loading Mode 1 Loading Mode 2 Loading Mode 3 Loading Mode Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode Cycles (N) Viscoelastic-Viscoplastic Constitutive Model Viscoelastic-Viscoplastic- Viscodamage Model Rutting (mm) Loading Mode 1 Loading Mode 2 Rutting (mm) Loading Mode 3 Loading Mode 4 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode Cycles (N) Loading Mode 1 Loading Mode 2 Loading Mode 3 Loading Mode 4 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode Cycles (N)

37 Application: Different Loading Modes and Constitutive Models 3D Rutting simulation results: Different constitutive models. Rutting (mm) 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 Cycles (N) 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 Loading Mode 5 Loading Mode 6 Loading Mode 7 Loading Mode 8 Loading Mode 9 Loading Mode 10 Loading Mode 11 Rutting (mm) Rutting (mm) Cycles (N) Viscoelastic-Viscoplastic- Viscodamage Model Cycles (N)

38 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.

39 Simulation Results Viscoplastic strain 2D Results 3D Results

40 Simulation Results Damage evolution 2D Results 3D Results

41 Compare with Experimental Data Rutting (mm) Experimental Measurements 2D results 3D results Cycles (N)

42 Applied stress (T=55 o C) ALF Data-Variable Stress Deviatoric stress (kpa) Time (Sec)

43 Model Validation: ALF Data (Strain Response) 1 st Cycle 2 nd Cycle 3 rd Cycle 4 th Cycle

44 Model Validation: ALF Data (Strain Response) 5 th Cycle 6 th Cycle 7 th Cycle 8 th Cycle

45 Model Validation: ALF Data (Strain Response) Model predictions at large loading cycles 4.50E E 03 exp cal. Total Strain 3.50E E E E 03 Deviatoric stress: 712kPa 1.50E 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.

46 Model Validation: ALF Data (Strain Response) Constant Stress-Variable Time Loading Viscoplastic VP strain Strain model exp Cycle

47 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.

48 THANK YOU Questions?