VECD (Visco-ElasticContinuum Damage): State-of-the-art technique to evaluate fatigue damage in asphalt pavements

Transcription

1 VECD (Visco-ElasticContinuum Damage): tate-of-the-art technique to evaluate fatigue damage in asphalt pavements M. Emin Kutay, Ph.D., P.E. Assistant Professor Michigan tate University

2 History of the Viscoelastic Continuum Damage (VECD) theory Beginnings Present Future chapery U. Texas, Austin Kim & Little Texas A&M Kim, Daniel, & Chehab CU Broader esearch: U of ebraska (Y.ak Kim), wedish oyal Inst. (Lunstrom & Isaacson), CHP 9-9 CU (Kim & Chehab) UMD (chwartz & Gibson), AAT LLC. (Christensen & Bonaquist), FHWA (Kim et al, Kutay et al)

3 What is VECD? VE.. Visco elastic ate dependent Fully recoverable..cd Continuum Damage A continuum is a body that can be continually sub-divided into infinitesimal small elements with properties being those of the bulk material.

4 What is VECD? Elastic Viscoelastic o Damage σ = E σ = E t ve = E( t t' ) dt ' E t' E-VE Corresp. Principle Pseudo train With Continuum Damage σ = C() σ = C( )

5 Damage characteristic curve (C vs ) C Modulus Proposed as a fundamental material property that governs damage growth under all conditions stress level, strain level, frequency / rate, and temperature. Damage Internal tate Variable

6 What can you do with C vs curve? odulus C Mo How do you get it? Damage Internal tate Variable

7 First input LVE characteristics E* (MPa) (a) T ref =9 o C Terpolymer B LG C-TB AB Fiber Control educed frequency, f (Hz) Max slope = m, α = /m T ref =9 o C (b) E* E(t) inter-conversion E (t) (MPa) Terpolymer B LG C-TB AB Fiber Control educed time, t (sec) 7

8 How to get C & VECD equations C C vs Pseudo-strain = E(t τ) dτ E τ x 5 tress-strain relation (E-VE correspondence principle) σ = C Energy equation σ W = W = 2 C 2 Damage evolution law d dt = W α

9 How to get C &.8 C vs Input: t, σ( t), ( t) & E( t) C.6.4 ( t + t) = t+ t E(t + t τ) τ dτ x 5 C( t + t) = σ ( t + t) ( t + t) α + α + t) = ( t) + t + [ ] 2.5 ( t) α ( C( t + t) C( )) ( t t

10 Drawbacks of past VECD approaches Monotonic tension likely requires force greater than capacity of the AMPT (a.k.a., PT) Convolution integral can be very time consuming t ( t) = E(t τ) dτ τ outine FE analysis for pavement design may not be practical (but strong basis for Performance elated pecifications (P))

11 Practical use of VECD : Cyclic Push-Pull Pull Fatigue Approach ee Also: Kutay, Gibson &Youtcheff AAPT 28

12 Uniaxial push push--pull = compression compression-tension fatigue tests Advantages: ample can be made in uperpave gyratory compactor imple uniaxial stress state Tests can be conducted using the Asphalt Mixture Performance Tester (AMPT, a.k.a. imple Performance TesterPT 2

13 Cyclic Push-Pull Fatigue Approach Well Poised For Implementation through AMPT (PT) This type of routine testing is now within the reach of tate DOTs and Contractors?

14 C & from peak-to-peak stresses and strains Input: * f, E, α,, σ, LVE E * = σ C = E* E* LVE = E* LVE + = + ( ) 2 + α + α ( ) f.5 C C + α Derivations are at Kutay, Gibson & AAPT 28

15 A simple Excel sheet is sufficient to obtain C & f (Hz). E* LVE (kpa) 656. T ( o C) 9. α (/n) 2.4 pec: AB_ I (Cycles) σ o (MPa) o avg E* (kpa) (kpa) σ (strain) C C (/C) σ σ E E E-.27E E E E E E-8.94E E E E E E E E E-9 4.2E E E E E E E E E-8 8.9E E E-8 9.5E E E-8.7E E E-8.9E E E-8.35E E E-8.53E E E-8.63E E E-9.72E E E-8.93E E E-8 2.E-7

16 C vs curve of the Control PG7-22 mixture at different temp., freq. and loading modes E* C = E* LVE C b a C = e ctrl, f=hz, T=9C ctrl, f=hz, T=9C σ ctrl, f=hz, T=9C σ ctrl, f=hz, T=9C σ ctrl, f=hz, T=25C [ ] α + α ( ) +α + = + 2 f.5 I ( C + C )

17 Is peak to peak C vs same as the C vs computed using the hereditary integral? 7

18 Validation methodology TEP () Calibrate model using peak-to-peak formulation : C vs was calculated using peak to peak stresses and strains. E* LVE * = C.8 AB (stress sweep) AB 2 (stress sweep) AB.6 3 (stress sweep) C=exp(-.44*^^.486) C = I E* E* LVE [ ] α e x 4 α 2 + ( ) + α + = + f.5 I ( C + C ) Fit C = exp(a b ) 8

19 Validation methodology TEP (2) imulate using the state-variable implementation of the hereditary integral:igorous simulation (input: time v.s. strain, output: stress) was performed using VECD state variable implementation. σ el i ( t) σ ηi tt [ e ] t / ρ t / ρi el i = e ( t t) + (stress in each Maxwell element i ( t) + n ( t) = E σ ( t) i= dc b b = exp(a(t) )a b(t) t C t + t = t + t 2 d ( ) ( ).5 I ( t) t b C( t + t) = exp( a( t + t) ) el i σ ( t + t) = I C( t + t) ( t + t) (pseudostrain) α at time t) 9

20 Validation methodology TEP (3) Validation (A) tress sweep testing at Hz, 9C 3 AB mall tress weep o nlyaverages-tress vs time 2 tress (kpa) - (stress in each Maxwell element at time t) -2-3 Predicted Measured educed Time (t) 2

21 Validation methodology TEP (3) Validation (B) crosshead strain controlled fatigue testing at Hz, 9C 5 AB9 7 8Microstrain s tressstrainphaseangle-tress vs time tress (kpa) Predicted Measured educed Time (t) C vs 2

22 Is peak to peak C vs same as the C vs computed using the hereditary integral? Answer: YE! 22

23 C vs curves of all mixtures E* C = E* LVE C C = exp(a b ) Control 7-22 AB CTB FIBE BLG Terpolymer [ ] α + α ( ) +α + = + 2 f.5 I ( C + C )

24 UE #: Finite Element Implementation esearch led by. Kim at CU with ALF materials

25 UE #2 imulation of uniaxial cyclic strain controlled tests (implified & More Practical) C = =, = =, E* = = E* LVE σ = = = E * _LVE d C = d exp (a b ) a b b- = + ( ) α dc + f 5 I 2. d α C b + = exp(a + ) = + = + E * C E* σ = * + + E + LVE

26 Validation of the applicability of VECD to push-pull fatigue tests E* (MPa) C-TB tested at 2C, 5Hz Predicted Measured ot used in the VECD calibration (cycles)

27 Push-pull fatigue simulation results (ALF Mixtures) E* (MPa a) Control722 AB CTB Fiber B-LG Terpolymer (Cycle o)

28 Comparison with field accelerated pavement testing data tructural rails 29 m a tructural rails uper-single truck tire b 28

29 Use #3: Fatigue life from the VECD and proposed MEPDG implementation

30 f in MEPDG vs. ALF cracking log ( ) - MEPD DG f f.8939 = ( 6.6) C H C t E.779 Control 7-22 AB Fiber B-LG E* at 9 o C 2.5Hz Used the bottom measured strain Local calibration constants Lane 2 PG 7-22 Lane 3 Air-blown Lane 4 B-LG a) b) c) 2.2 CTB Terpolymer log ( ) at ALF 2%

31 umber of cycles to failure ( f ): General form of the equation d d f 2 dc = 2 d α f f = 2 2 dc d α f d 2 2 dc d α f d = d = E* LVE α 2 dc f d = 2 d f f d f = f = 2 E 2 * 2 LVE dc d at α f eference: Kutay et al. TB 29

32 Closed-form solutions of the f equation for special cases * Christensen & Bonaquist = α ** Lee et al. 2 α f ( C ) ( α C ) + α 2α 2α 2 E * LVE ( C ) C = exp 2 C C vs x 5 * Christensen, D. W. and Bonaquist,. F. (25). Practical application of continuum damage theory to fatigue phenomena in asphalt concrete mixtures. J. Assn. of Asphalt Paving Technologists, Vol.74, pp ** Lee, H. J., Daniel J.., and Kim, Y.. (2) Continuum damage mechanics based fatigue model of asphalt concrete. J. Mater. Civ. Eng., 2(2), 5 2.

33 General form of the VECD- f equation f = f = 2 E 2 * 2 LVE dc d at α f Procedure: elect the C() function that best fits to given data elect failure criterion, e.g., C=.5, strain level ( ) and E* LVE Calculate f corresponding to C=.5 Calculate f using equation above.

34 Proposed MEPDG implementation Level input (using AMPT) E* master curve Push-pull test at a specified temperature and frequency (e.g., 5 o C, Hz)

35 Possible use of VECD in MEPDG for remaining service life

36 Comparison with field accelerated pavement testing data tructural rails 29 m a tructural rails uper-single truck tire b f = f = 2 E 2 2 * LVE dc d at α f 36

37 M. EminKutay, Ph.D., P.E. Assistant Professor Michigan tate University Department of Civil & Environmental Engineering 37

38 Correlation of VECD-fwith field-different load levels: 38

39 Prediction of fatigue life f = f = 2 E 2 * 2 LVE dc d at α f.8 C vs dc d at C.6 C f(failure) f(failure) x 5 39

40 pecimen size limitation Traditional specimen sizes: or 75 mm diameter, 5 mm tall Thin pavements (thickness< 5mm) are not suitable for field core testing olution (?) mall diameter & small height samples Horizontal coring from the field slabs 4

41 Can small size samples work? egular ize () D = 7.4 mm, H =5 mm mall ize () D = 38. mm, H= mm C () ctrl () ctrl2 () ctrl3 σ () ctrl σ () ctrl2 σ () ctrl3 σ () ctrl () ctrl2 () ctrl3.2 (a) Air Blown Answer: Yes! eference: Kutay, Gibson & TB 29 4

42 ext step after obtaining C & Develop the relationship by fitting a simple equation C (a) C = e a b ctrl-, Hz, 9C, Hz, 9C ctrl-2 Hz, 9C ctrl-3 σ ctrl-, Hz, 9C σ ctrl-2, Hz, 9C σ ctrl-3, Hz, 9C σ ctrl, 5Hz, 2C