Pavement Distress Modes Strain Componentsschwartz/presentations/unnctam14_2002.… · Strain Components in Asphalt Concrete C.W. Schwartz (UMD) J. Uzan (Technion) N.H. Gibson (UMD)

1

Time-TemperatureSuperposition of

Strain Componentsin Asphalt Concrete

C.W. Schwartz (UMD)J. Uzan (Technion)N.H. Gibson (UMD)M.W. Witczak (ASU)

USNCAM14Blacksburg, VA

June 24-28, 2002

Pavement Distress ModesPavement Distress Modes

d

Permanent Deformation

Fatigue CrackingThermal Cracking

+ ReflectionCracking

Material Characterization Models:Material Characterization Models:Pavement SystemPavement System

Strain

Stress

Strain

Log εp

Log N

Log εp

Log N

Stress

Time

Stress Nonlinearity Cyclic Loading

Time EffectsViscoelasticityViscoplasticity

+ Temperature, MoistureDependence

Problem ContextProblem Context

• Comprehensive material model for AC must span allbehavior phenomena:

ViscoelasticityMicrostructural damage (and damage localization)Viscoplasticity

• Major variables:TemperatureRate of loadingStress state

Theoretical BackgroundTheoretical Backgroundεt = (εve + εd) + εvpεt = (εve + εd) + εvp

Strain Decomposition

Schapery Schapery Continuum Damage ModelContinuum Damage Model

• εt = total strain• εve = viscoelasticity (linear recoverable)• εd = microstructural damage (nonrecoverable rate-

independent)• εvp = viscoplasticity (nonrecoverable rate-dependent)

Additional consideration: Post-peak localization (macrofracture)

2

ViscoelasticityViscoelasticity

0 0

1 ( ) t

ijRij

R T

dtE dE a

ξ ∂ε ′′ ′ε = ξ − ξ ξ ξ =

′∂ξ∫ ∫

Correspondence Principle:

• εijR = Pseudo-strain

• E(t) and aT(T) = material properties

MicrostructuralMicrostructural Damage Damage

Damage D = SD/S0≤D ≤1

( ) ( )D ii

W S f S∂σ ≡ = ε

∂ε

( 1, 2)m

m D

m

S W mt S

α ∂ ∂

= − = ∂ ∂ in which: αm = material properties

Damage Evolution Law:

Stress-Strain Relation:

in which: WD = energy density Si = internal state variables f(Si) = damage functions

ViscoplasticityViscoplasticity

Strain-Hardening Model:

( ) ( )1 11 11 11 11 11 1

( )

( )

1 1

vp pvp

q

p pq qp pp pvp

gA

g B

p pB t tA D

σεε

σ σ

ε σ σ+ ++ ++ +

=

=

+ + = =

• D, p, q = material properties

Problem StatementProblem Statement

• Material characterization requires extensive laboratorytesting

• “Brute force” approach (w/ exaggeration): 3 Temperatures x 3 Loading rates x 3 Deviator stresses x 2 Confining pressures x 3 Types of tests 162 Tests

How can this be reduced???How can this be reduced???

Time-Temperature Superposition ConceptsTime-Temperature Superposition Concepts

Log (Loading Time)

Log

(Stif

fnes

s)

T1 T2T0

t / aT1 t / aT2

““ThermorheologicallyThermorheologically Simple Material” Simple Material”-5

-3

-1

1

3

-10 10 30 50 70Temperature, °C

log

(aT)

5 °C25 °C40 °C60 °CPredicted

-5

-3

-1

1

3

-10 10 30 50 70Temperature, °C

log

(aT)


0

1

10

100

-7 -5 -3 -1 1 3 5 7Log (Reduced Time) [sec]

Dyn

amic

Mod

ulus

E*

[Gpa

]


0

1

10

100

-7 -5 -3 -1 1 3 5 7Log (Reduced Time) [sec]

Dyn

amic

Mod

ulus

E*

[Gpa

]


Typical Results:Typical Results:FrequencyFrequency

SweepSweep

12.5 mm MSHASuperpave mix

Master Curve

Temperature Shift

Stress

Strain

Phase lag

Time

Stress

Strain

Phase lag

Time0

0*εσ

=E

3

Key QuestionsKey Questions

• Do time-temperature superposition concepts continue toapply to AC under non-small strain conditions?

• Do similar rate processes apply to different components ofthe material response?

ViscoelasticityDamage (micro/macro)Viscoplasticity

Constant Strain Rate TestsConstant Strain Rate Tests

12.5 mm MSHASuperpave mix

Strain

Time

ε

Temperature T

Test FactorialSee

Schwartz et al.TRB 2002

Unconfined Compression, 25oC

0.00

0.01

0.02

0.03

0.04

0.05

0 20 40 60 80 100Time (sec)

Stra

in


0.00

0.01

0.02

0.03

0.04

0.05

0 20 40 60 80 100Time (sec)

Stra

in


0

2000

4000

6000

8000

0.00 0.01 0.02 0.03 0.04 0.05Strain

Stre

ss (k

Pa)

0.00050.00150.00450.0135ReplicateReplicate


0

2000

4000

6000

8000

0.00 0.01 0.02 0.03 0.04 0.05Strain

Stre

ss (k

Pa)

0.00050.00150.00450.0135ReplicateReplicate

ConstantConstantCrossheadCrossheadRateRate

ε

σ

ε

σ

ε

σ

T1 T2 T3

C

B

A

F

ED

GH

IIncreasingStrain Rate

IncreasingStrain Rate

IncreasingStrain Rate

ε1 ε1 ε1

log t

log σ

ε = ε1

T1

T2

T3

A

D

G

B

E

H

C

F

I

Cross-Plotting Methodology - Part 1Cross-Plotting Methodology - Part 1

Cross-Plotting Methodology - Part 2Cross-Plotting Methodology - Part 2

log t

log σ

ε = ε1

T1

T2

T3

A

D

G

B

E

H

C

F

I

log tR

log σε = ε1

T0 = T2

log aT

T

ε = ε1

T1

T2

T3

ε = 0.0025

100

1000

10000

100000

-4 -2 0 2 4 6

Log Reduced Time (sec)

Stre

ss (k

Pa)

5 C 25 C 40 C 60 C

ε = 0.0025

100

1000

10000

100000

-4 -2 0 2 4 6


Stre

ss (k

Pa)

5 C 25 C 40 C 60 C

ε = 0.0125

100

1000

10000

100000

-2 0 2 4 6


Stre

ss (k

Pa)

ε = 0.0125

100

1000

10000

100000

-2 0 2 4 6


Stre

ss (k

Pa)

ε = 0.0200

100

1000

10000

100000

-2 0 2 4 6

Log Reduced Tim e (sec)

Stre

ss (k

Pa)

ε = 0.0200

100

1000

10000

100000

-2 0 2 4 6

Log Reduced Tim e (sec)

Stre

ss (k

Pa)

Cross-PlottingCross-PlottingResultsResults Early

Response

Peak RegionPost-Peak

4

Stress Master CurvesStress Master Curves

100

1000

10000

100000

-2 0 2 4 6log Reduced Time (sec)

Stre

ss (k

lPa)

0.00250.00500.00750.01000.01250.01500.01750.02000.02250.0250

Increasing Strain Level

100

1000

10000

100000

-2 0 2 4 6log Reduced Time (sec)

Stre

ss (k

lPa)

0.00250.00500.00750.01000.01250.01500.01750.02000.02250.0250


Temperature Shift FactorsTemperature Shift Factors

-5

-4

-3

-2

-1

0

1

2

3

0 10 20 30 40 50 60 70

Temperature (oC)

log

a T

Freq.Sweeps0.00250.00500.00750.01000.01250.01500.01750.02000.02250.0250



-5

-4

-3

-2

-1

0

1

2

3

0 10 20 30 40 50 60 70

Temperature (oC)

log

a T

Freq.Sweeps0.00250.00500.00750.01000.01250.01500.01750.02000.02250.0250



Large Strain Temperature Shift

0

1

10

100

-7 -5 -3 -1 1 3 5 7Log Reduced Time, sec

E* [

Gpa

] 5 °C25 °C40 °C60 °CPredicted

Large Strain Temperature Shift

0

1

10

100


E* [

Gpa

] 5 °C25 °C40 °C60 °CPredicted

Small Strain Temperature Shift

0

1

10

100


E* [

Gpa

]


Small Strain Temperature Shift

0

1

10

100


E* [

Gpa

]

5 °C25 °C40 °C60 °CPredictedR2 = 0.99

R2 = 0.98

Strain influenceon aT is notsignificant?

ViscoplasticViscoplastic Creep and Recovery Tests Creep and Recovery Tests

Time

Load

T ime

Load

T ime

Load

T ime

Load

Constant Stress/Increasing Time

• Determines time exponent p

Increasing Stress/Constant Time

• Determines stress exponent q

Confirmation of LargeConfirmation of LargeStrain Time-TemperatureStrain Time-TemperatureSuperposition:Superposition:Creep and RecoveryCreep and RecoveryTestsTests

0.00.20.40.60.81.01.2

0 50 100Reduced Time

Load

Low Temperature High Temperature

0.00.20.40.60.81.01.2

0 50 100Reduced Time

Load

Low Temperature High Temperature

Low Temperature

0.00.20.40.60.81.01.2

0 50 100Time

Load

Low Temperature

0.00.20.40.60.81.01.2

0 50 100Time

Load

High Temperature

0.00.20.40.60.81.01.2

0 50 100Time

Load

High Temperature

0.00.20.40.60.81.01.2

0 50 100Time

Load

(Large-strain temperature shift)

25o and 35o C

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 1000 2000 3000 4000 5000Reduced Time, sec

Stra

in, % 35C (Shifted)

25C (Unshifted)

25o and 35o C

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 1000 2000 3000 4000 5000Reduced Time, sec

Stra

in, % 35C (Shifted)

25C (Unshifted)

35oand 45oC

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 500 1000 1500 2000Reduced Time, sec

Stra

in, %

45C (Shifted)35C (Unshifted)

35oand 45oC

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 500 1000 1500 2000Reduced Time, sec

Stra

in, %

45C (Shifted)35C (Unshifted)

Creep andCreep andRecoveryRecovery

Confirmstime-temperature

superposition.

5

Viscoplasticity Viscoplasticity ParametersParameters

0.0001

0.001

0.01

0.0001 0.001 0.01

Measured Viscoplastic Strain (mm/mm)

Pred

icte

d Vi

scop

last

ic S

trai

n

25C & 35C 'Fixed Stress' Data

35C 'Fixed Time' Data

35C & 45C Verification 'FixedStress' Data

0.0001

0.001

0.01

0.0001 0.001 0.01

Measured Viscoplastic Strain (mm/mm)

Pred

icte

d Vi

scop

last

ic S

trai

n

25C & 35C 'Fixed Stress' Data

35C 'Fixed Time' Data

35C & 45C Verification 'FixedStress' Data

D = 1.30E+15p = 1.53q = 2.09

( )1 111 111 p q pp

vpp tD

ε σ+ +++ =

Verification -Creep and Recovery

25oC, σ ≅ 1500 kPa

Replicate 1

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500Time (sec)

Stra

in

Measured TotalVE + DamageVPComputed Total

Replicate 1

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500Time (sec)

Stra

in


Replicate 3

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (sec)

Stra

in


Replicate 3

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (sec)

Stra

in


Replicate 2

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (sec)

Stra

in


Replicate 2

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (sec)

Stra

in


0.0005/sec (Replicate 1)

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 5 10 15 20 25

Time (sec)

Stra

in



0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 5 10 15 20 25

Time (sec)

Stra

in



0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 1 2 3 4 5 6 7 8 9

Time (sec)

Stra

in



0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 1 2 3 4 5 6 7 8 9

Time (sec)

Stra

in


0.0045 (Replicate 2)

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)

Stra

in


0.0045 (Replicate 2)

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

0 0.5 1 1.5 2 2.5 3 3.5

Time (sec)

Stra

in



0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

1.0E-02

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Stra

in

Me a su r e d To t a lVE + Da m a g eVPCo m p u t e d To t a l


0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6.0E-03

7.0E-03

8.0E-03

9.0E-03

1.0E-02

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Stra

in

Me a su r e d To t a lVE + Da m a g eVPCo m p u t e d To t a l

Verification: Constant Strain Rate (25oC)ConclusionsConclusions

• Time-temperature superposition appears to remain valid atvery large strains

Confirming data from tension CSR, creep-and-recovery tests(Kim/NCSU)Confirming trends from repeated load permanent deformation,static creep tests (Witczak/ASU)

• Enhanced Schapery continuum damage model captures thekey aspects of asphalt concrete behavior (pre-localization)

ViscoelasticityMicrostructural damageViscoplasticity

• Validation against independent laboratory tests isunderway

Pavement Distress Modes Strain Componentsschwartz/presentations/unnctam14_2002.… · Strain Components in Asphalt Concrete C.W. Schwartz (UMD) J. Uzan (Technion) N.H. Gibson (UMD)

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