Caracterizacion fatiga y daño

8/12/2019 Caracterizacion fatiga y dao

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doi: 10.1111/j.1460-2695.2005.00949.x

Characterization of fatigue damage for paving asphaltic materials

I . A R T A M E N D I a n d H . K H A L I D

Department of Civil Engineering, University of Liverpool, Brownlow Street, L69 3GQ, Liverpool, UK

Received in final form 20th May 2005

A B S T R A C T This study investigates the fatigue characteristics of typical bituminous materials usedin road applications. Fatigue testing was performed in a four-point bending beam testapparatus under controlled strain and stress conditions. Fatigue life was defined using theclassical approach as the number of cycles, Nf, to 50% reduction in the initial stiffnessmodulus. It has also been defined in terms of macro-crack initiation, N1. A differentapproach,basedon thelinear reductionin stiffnessduring a particular stage of a fatigue test,

was introduced to define a damage parameter, and the evolution of this damage parameterwith number of cycles was used to characterize fatigue life. Furthermore, refinementsto the linear damage model were introduced to take into account the difference in the

evolution of dissipated energy between controlled strain and stress testing modes. Thesemodifications have enabled the identification of a unique fatigue damage rate for bothcontrolled strain and stress test modes.

Keywords bituminous materials; dissipated energy; fatigue life; four-point bendingtest; linear damage model.

N O M E N C L A T U R E D = damage parameterE= complex stiffness modulus (referred as stiffness)

E0 = initial stiffnessE00 = intercept of the fitted line for the stiffness data

N= number of (load) cyclesNf= number of cycles to 50% stiffness reduction

N1 = number of cycles to macro-crack initiationRn = energy ratioW= dissipated energy

W00 = intercept of the fitted line for the dissipated energy datan = strain at the n-cyclen = stress at the n-cyclen = phase angle at the n-cycle

I N T R O D U C T I O N

Fatigue cracking is one of the major load-related distressesexperienced in asphalt pavements and occurs when a bi-

tuminous layer is subjected to repeated loading under thepassing traffic. In the laboratory, fatigue life is typicallyassessed by repeated load bending tests. Three configura-tions are mainly employed, two-point bending or trape-zoidal beam test, and three- or four-point bending tests.

Fatigue tests are normally carried out in either con-trolled strain or controlled stress mode.1 In controlled

Correspondence: I. Artamendi. E-mail: [email protected] paper is based on a presentationmade at the ECF15 Conference,August2004, Stockholm, Sweden.

strain mode, the strain is kept constant by decreasing thestressduring the test whereas in controlled stressthe stressis maintained constant, which increases the strain duringthe test. In general, controlled stress testing has been re-

lated to relatively thick pavement construction where highstiffness is the fundamental parameter that underpins fa-tigue life. Controlled strain testing, on the other hand,has been associated with thin conventional flexible pave-ments where the elastic recovery properties of the mate-rial have a fundamental effect on its fatigue life.2 Some

workers, however, have alluded to a combined strain andstress mode control.3 This is not strictly a pure fatiguetest, if not a fracture test, usually associated with met-als. In this fracture test, the sample is loaded repeatedly

c 2005 Blackwell Publishing Inc. Fatigue Fract Engng Mater Struct 28, 11131118 1113


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1114 I . A R T A M E N D I a n d H . K H A L ID

until a crack appears and this is continued until collapseoccurs.

Different approaches have been used to define the fa-tigue life of bituminous materials. Failure in controlledstrain has been widely defined as 50% reduction in theinitial stiffness modulus.4 For controlled stress testing,

on the other hand, fatigue failure has been traditionallyconsidered to occur when the modulus is at 10% of itsoriginal value.5 These definitions, however, are consid-ered arbitrary and do not represent the internal state ofthe material.

Hopman et al.6 and Pronk7 introduced an energy ra-tio, R n, based on the dissipated energy concept and de-fined failure as the number of cycles, N1, where cracksare considered to initiate; it has also been defined as thecoalescence of micro-cracks to form a sharp crack, whichthen propagates.8 Thus, this point represents the transi-tion point between micro-crack formation and the propa-gation of a macroscopic crack. In controlled strain mode,

whenRnis plotted against the number of cycles,N1is de-finedas the point where the slope ofRnagainstNdeviatesfrom a straight line. In controlled stressmode,on theotherhand,N1 corresponds to the peak value ofR n. For con-trolled strain and stress modes,N1represents the materialin the same state of damage corresponding to macro-crackinitiation.8 It is, however, more difficult and subjective toaccurately define the N1 point for strain mode than forstress mode. Furthermore, evidence for crack initiation at

N1 has been previously confirmed in an earlier work byTam.9

Di Benedettoet al.1,10 proposed a different approach to

characterize fatigue. They identified the existence of astage during a fatigue test, which accountedfor most of thefatigue life, where the reduction in the stiffness with num-ber of load applications was approximately linear. Based

Fig. 1 Four-point bending test apparatus and test configuration.

on this, a damage parameter (D) was introduced and thechange in this parameter with number of cycles has beenused to depict damage due to fatigue. Furthermore, themodel proposed by Di Benedettoet al. introduced an en-ergy term to counteract the variability due to dissipatedenergy effects in the two modes of loading.

The objective of this paper is to investigate the fa-tigue characteristics of two typical bituminous materials,namely dense bitumen macadam (DBM) and stone masticasphalt (SMA), used in road applications in the UK. Theenergy ratio and linear damage evolution approaches usedto depict fatigue life have been applied and compared withthe arbitrary approach.

F AT I G U E T E S T P R O C E D U R E S

Fatigue testing was performed in a four-point bending(4PB) test apparatus shown schematically in Fig. 1. Thetest equipment consisted of a servo-hydraulic actuator

connected to a 2.5 kN load cell mounted above the fa-tigue frame. The load was applied through the actuatorthat was connected to the fatigue frame by means of asteel shaft. Once inserted the specimen was clamped inposition at the four points of the fatigue frame by meansof torque motors located underneath the four supports.The vertical deflection at the centre of the beam was

measured using a linear variable differential transducer(LVDT) situated at the bottom of the beam. The trans-ducer waspushed into contact with the specimen by meansof a pneumatically controlled trigger mechanism priorto start of the test. The vertical deflection and the ap-

plied load were used to calculate the strains and stresses.Furthermore, phase angle, dissipated energy and cumu-lative dissipated energy were also computed during thetest.

c 2005 Blackwell Publishing Inc. Fatigue Fract Engng Mater Struct 28, 11131118


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C H A R AC T E R IZ A TI O N O F F AT I G U E D A MA G E 1115

Fig. 2 Definition of failureNfin controlled strain and stress test

modes.

Beam specimens of 300 50 50 mm3 were cut from

300 300 mm2

slabs manufactured in the laboratory andused for fatigue testing. All tests were conducted at a tem-perature of 10 C and 10 Hz frequency, under sinusoidalloading with no rest periods. Testing was carried out un-der controlled strain and stress conditions. For controlledstrain testing, strain amplitude levels selected varied be-tween 125 and 200 m/m. For controlled stress testing,stress amplitude levels selected varied between 1.25 and2 MPa.

C H A R A C T E R I Z A T I O N O F F A T I G U E L I F E

Definition of failure based on stiffness reduction

Fatigue failure has been arbitrarily defined as the numberof cycles, Nf, at which the initial stiffness is reduced by50%, forboth controlled strainand stresstest modes. Typ-ical fatigue data from 4PB tests for controlled strain andstress tests are presented in Fig. 2. This data correspondto two DBM beam specimens under similar initial strainconditions of 153 and 152.2 m/m. It can be seen that,under these conditions, failure in controlled stress modeoccurred considerably earlier than in controlled strainmode.

Fatigue test data in controlled strain and stress modehave been used to derive a relationship between the initialstrain, 0, defined as the strain at 100 cycles,

1 and fatiguelife,Nf, as shown in Fig. 3. It is customary to evaluate thematerials initial properties, e.g. modulus and phase angle,at 100 cycles, as there has been a consensual agreementthat this point, i.e. 100 cycles, represents a statisticallyreliable condition where the material is at its most un-damaged state.1 It can be observed that, firstly, fatigue lifefor the SMA material was longer than that for the DBMmaterial, independent of the test mode and, secondly,fatigue lives from controlled stress tests were shorter

than those from controlled strain tests for both materi-als. Longer lives for the SMA material are attributed to

volumetric composition and type of bituminous binder.Shorter lives in controlled stress mode are due to higherrate of crack propagation in this mode as it is a function ofthe stress magnitude at the crack tip. In controlled strain

mode, on the other hand, there is a gradual reduction inthe applied stress as the material weakens.

Definition of failure based on energy ratio

An energy ratio,Rn, has been used to define the number ofcycles,N1, where macro-cracks are considered to initiate.

The energy ratio is defined as the quotient between thecumulative dissipated energy up to the n-cycle and thedissipated energy at the n-cycle. Thus,

Rn =

n

i=0iisin i

nnsin n , (1)

where , and are the stress, strain and phase angle,respectively.

Figure 4 shows the evolution ofRn with number of cy-cles for the two specimens presented in Fig. 2. It can beseen that for controlled strain mode, when R n is plottedagainst the number of load cycles there is a change in be-haviour atN1 represented by the change of the slope atthis point. The accurate determination ofN1is, however,somewhat subjective. In controlled stresstest mode, on theother hand,N1corresponds to the peak value whenRnisplotted against the number of load cycles. Furthermore,under similar initial strain conditions,N1is lower for con-trolled stress than for controlled strain mode, as shown inFig. 4. Also, crack initiation, indicated byN1, occurredbefore the attainment of 50% reduction in stiffness, i.e. at

Nf.

Fig. 3 Relationship between fatigue lifeNfand initial strain.



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Fig. 4 Definition of failureN1in controlled strain and stress test

modes.

Fig. 5 Relationship between fatigue lifeN1and initial strain.

The relationship between N1 and the initial strain forcontrolled strain and stress tests is presented in Fig. 5. Itcan be seen that, again, the SMA material had longer fa-tigue life than the DBM for both test modes, and similarlyfatigue life,N1, for controlled stress mode was shorterthan for controlled strain. Furthermore, the scatter ob-served in Fig. 5 (and Fig. 3) is representative of typicalscatter inherent in fatigue test results.Although fatigue tests gave similar relationships for

N1 and Nf, the N1 failure criterion allows a compari-son of materials at equal states of damage, correspondingto macro-crack initiation, and avoids arbitrary definitionof failure.

Definition of fatigue damage

Fatigue data from 4PB tests have shown the existence ofa stage during the test characterized by an approximatelylinear reduction in the stiffness modulus,E, with numberof cycles, as shown in Fig. 2. Based on this linear reduction

Fig. 6 Relationship between rate of damage dD/dNand initial

strain.

in the stiffness a damage parameter,D, can be introduced.

Thus,

D(N) =E00 E(N)

E00. (2)

The rate of damage evolution can be calculated by differ-entiating Eq. (2),

dD

dN=

1

E00

dE

dN= aT, (3)

whereE00 and dE/dNare the intercept and the slope ofthe fitted line for the stiffness data, as shown in Fig. 2.The relationship between dD/dNand the initial strain

for both test modes was approximated by a power law,which gave regression coefficients (R2) of about 0.8 forboth tested materials. These relationships are presentedin Fig. 6. It can be observed that, as expected, for thesame initial strain, the rate of damage evolution for con-trolled stress tests is higher than that for controlled straintests. It can also be seen that the rate of damage evolutionfor the DBM material is higher than that for the SMAmaterial, independent of test mode. These observationsare attributed to the same reasons given in the previoussection.

Differences between the rate of damage evolution forcontrolled strain and stress tests have been attributed todissipated energy effects occurring in both test modes.1,10

During controlled strain fatigue testing the dissipated en-ergy decreases with Nand increases during controlledstress tests, as shown in Fig. 7. Furthermore, under similarinitial strain conditions, the rate of change (slope) in dis-sipated energy per cycle (Wn = nnsin n) with loadcycles is faster for controlled stress than for controlledstrain mode (see Fig. 7).As a result of the energy differences, the proposed re-

lationship to determine the corrected rate of damage



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C H A R AC T E R IZ A TI O N O F F AT I G U E D A MA G E 1117

Fig. 7 Evolution of dissipated energy in controlled strain and stress

test modes.

Fig. 8 Relationship between the parameteraWand the initialstrain.

evolution, dD/dN, can be expressed as follows:1

dD

dN = aT C

E0 E00

E00

aW, (4)

where E0 is the initial stiffness; C is a constant intro-duced to counteract the conflicting dissipated energy ef-fects from strain and stress mode tests, which depends onthe material and on specimen geometry; and aWis definedas follows:

aW=

1

W00

dW

dN,

(5)

whereW00and dW/dNare the intercept and the slope ofthe fitted line for the dissipated energy data, as shown inFig. 7.

Figure 8 shows a power law relationship between aW(absolute values) and the initial strain for both controlledstrain and stress tests, which gave R2 values between0.7 and 0.9. It can be seen thataWvalues for controlledstress tests are higher than for controlled strain tests, asexplained earlier (see Fig. 7). Moreover, aW values for

Fig. 9 Relationship between the corrected rate of damage

evolution dD/dNand the initial strain.

the DBM material are higher than those for the SMA

material.Finally, a power law relationship was found between the

corrected rate of damage evolution, dD/dN, calculatedusing Eq. (4), and the initial strain for both test modes.

The only remaining unknown parameter in Eq. (4) is theconstantC. In this work, a simple but new technique hasbeen developed for the determination of this constant.

The evaluation procedure involves assuming an initialvalue of zero for C. This is followed by an iterative in-cremental process that aims at maximising the R2 valuefor the power law relationship from the two sets of data,i.e. strain and stress. The values of the constantCdeter-

mined in this way were 1.95 and 2.05 for the DBM andSMA materials, respectively, which gave R2 values of 0.8for both materials.The relationship between dD/dNand initial strain for

controlled strain and stress tests for the two materials in-vestigated is presented in Fig. 9. The figure shows a uniquedamage relationship for each material, irrespective of testmode.

C O N C L U S I O N S

Fatigue results presented in terms of Nf and N1 havedemonstrated that fatigue lives could be presented in ei-ther format, althoughN1 is more preferable as it relatesto an internal state of the material. The interpretationofN1 from either test mode, however, is prone to somesubjectivity.A simple, new technique has been developed for the

evaluation of the constantCin the linear fatigue damagemodel proposed by Di Benedetto. The newly developedfatigue damage model and the dissipated energy approachhave ranked the SMA and DBM materials in the sameorder as the more classical approach, N f. However, the



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dissipated energy and linear damage evolution approachesare based on fundamental concepts, pertinent to a macro-structural damage condition of the material, and not onan arbitrary definition of failure, as the case is with theclassical approach. Moreover, the corrected rate of dam-age evolution approach is useful in depicting the materials

fatigue behaviour in that it identifies a unique damage rateindependent of the test mode.The results presented in this paper have contributed fur-

ther to the validation of the principle on which the previ-ously proposed fatigue damage depiction was based. Thiscontribution is manifested by widening the application totwo materials of markedly different design philosophies.It, therefore, gives more credence to the proposed tech-nique and, more importantly, provides much needed ad-ditional results to the database, generated independentlyof any previous work.

Acknowledgement

This work formed part of a research programme fundedby the UK Engineering and Physical Sciences ResearchCouncil and supported by a number of industrial partnersincluding Tarmac, J Allock & Sons and Shell, to whomthe authors are indebted.

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