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
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)
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.
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( )
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
What can you do with C vs curve? odulus C Mo How do you get it? Damage Internal tate Variable
First input LVE characteristics E* (MPa) (a) T ref =9 o C Terpolymer B LG C-TB AB Fiber Control 7-22 -5.. 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 -7. 8 educed time, t (sec) 7
How to get C & VECD equations C.8.6.4 C vs Pseudo-strain = E(t τ) dτ E τ.2 2 3 4 5 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
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.2 2 3 4 5 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
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))
Practical use of VECD : Cyclic Push-Pull Pull Fatigue Approach ee Also: Kutay, Gibson &Youtcheff AAPT 28
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
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?
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 & Youtcheff @ AAPT 28
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.7562878 (Cycles) σ o (MPa) o avg E* (kpa) (kpa) σ (strain) C C (/C) σ σ.93 3.88E-5 49624.6 254.58.29.. 2.248 5.E-5 49682.2 328.26.38...77.7..27E-.27E- 3.27 5.52E-5 49745.8 36.98.4.99 -.89 38.336 39.4. 6.85E-9 6.98E-9 4.29 6.2E-5 48395.2 395.9.44.97 -.76 7.3 9.7.2.24E-8.94E-8 5.36 6.57E-5 489764.2 43.2.48.97 -.4 28.342 37.4. 5.8E-9 2.45E-8 6.338 7.9E-5 4767497. 465.33.52.96 -.85 52.84 9.25. 9.45E-9 3.39E-8 7.36 7.58E-5 4746788. 497.5.55.96 -.42 35.42 225.3. 6.28E-9 4.2E-8 8.382 8.5E-5 469276.3 534.73.58.95 -.9 76.565 3.86..37E-8 5.39E-8 9.43 8.66E-5 465522.2 568.49.6.94 -.76 64.762 366.62..6E-8 6.55E-8.42 9.4E-5 463999.2 599.73.64.93 -.3 86.52 453.3..54E-8 8.9E-8.443 9.7E-5 456473.4 636.59.67.92 -.8 79.7 532.24..4E-8 9.5E-8 2.468.3E-4 4536579.7 677.24.7.9 -.55 66.3 598.55..9E-8.7E-7 3.49.9E-4 4595.7 72.6.75.9 -.5 67.478 666.3..2E-8.9E-7 4.53.5E-4 4478648.6 75.57.78.9 -.65 86.422 752.45..55E-8.35E-7 5.53.9E-4 44424.7 783.95.8.89 -.78 3.8 856.25..86E-8.53E-7 6.554.25E-4 4425322.2 82.23.84.89 -.3 55.926 92.8..E-8.63E-7 7.578.3E-4 44488.2 859.2.88.89 -.2 46.986 959.6. 8.44E-9.72E-7 8.594.36E-4 4378763.3 889.44.9.88 -.73 8.225 77.39. 2.E-8.93E-7 9.66.42E-4 435248.2 929.24.94.88 -.53.78 78...8E-8 2.E-7
C vs curve of the Control PG7-22 mixture at different temp., freq. and loading modes E* C = E* LVE C.8.6.4.2 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 5 4 5.5 5 2 5 [ ] α + α ( ) +α + = + 2 f.5 I ( C + C )
Is peak to peak C vs same as the C vs computed using the hereditary integral? 7
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.4.2 2 4 6 8 2 e x 4 α 2 + ( ) + α + = + f.5 I ( C + C ) Fit C = exp(a b ) 8
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) d @ t C t + t = t + t 2 d ( ) ( ).5 I ( t) d @ 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
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 -4 2 4 6 8 2 4 educed Time (t) 2
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) 5-5 - Predicted Measured -5 2 4 6 8 2 4 6 8 educed Time (t) C vs 2
Is peak to peak C vs same as the C vs computed using the hereditary integral? Answer: YE! 22
C vs curves of all mixtures E* C = E* LVE C.8.6.4.2 C = exp(a b ) Control 7-22 AB CTB FIBE BLG Terpolymer 5 4 5.5 5 2 5 [ ] α + α ( ) +α + = + 2 f.5 I ( C + C )
UE #: Finite Element Implementation esearch led by. Kim at CU with ALF materials
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
Validation of the applicability of VECD to push-pull fatigue tests E* (MPa) 4 35 3 25 2 5 5 C-TB tested at 2C, 5Hz Predicted Measured ot used in the VECD calibration 2 4 6 8 4.2 4 (cycles)
Push-pull fatigue simulation results (ALF Mixtures) E* (MPa a) 8 7 6 5 4 Control722 AB CTB Fiber B-LG Terpolymer 3 2 2 4 6 (Cycle o)
Comparison with field accelerated pavement testing data tructural rails 29 m a tructural rails uper-single truck tire b 28
Use #3: Fatigue life from the VECD and proposed MEPDG implementation
f in MEPDG vs. ALF cracking log ( ) - MEPD DG f 2.7 2.6 2.5 2.4 2.3 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 2. 4.4 4.6 4.8 5 5.2 5.4 5.6 log ( ) at ALF 2%
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
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.8.6.4 C vs.2 2 3 4 5 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. 963-2. ** 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.
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.
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)
Possible use of VECD in MEPDG for remaining service life
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
M. EminKutay, Ph.D., P.E. Assistant Professor Michigan tate University Department of Civil & Environmental Engineering kutay@msu.edu 37
Correlation of VECD-fwith field-different load levels: 38
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).4.2 2 3 4 5 f(failure) x 5 39
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
Can small size samples work? egular ize () D = 7.4 mm, H =5 mm mall ize () D = 38. mm, H= mm C.8.6.4 () ctrl () ctrl2 () ctrl3 σ () ctrl σ () ctrl2 σ () ctrl3 σ () ctrl () ctrl2 () ctrl3.2 (a) Air Blown 6.25 4.25 5.875 5 2.5 5 Answer: Yes! eference: Kutay, Gibson & Youtcheff @ TB 29 4
ext step after obtaining C & Develop the relationship by fitting a simple equation C.8.6.4.2 (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 7.5 4.5 5 2.25 5 3 5