单击此处编辑母版标题样式 Investigation into the Size effect on Four Point Bending Fatigue Tests

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1 单击此处编辑母版标题样式 Investigation into the Size effect on Four Point Bending Fatigue Tests Ning Li Ph.D. Candidate Presented to: the 3rd 4PBB Conference Co-authors: Ir. A.C. Pronk Prof. Dr. ir. A.A.A. Molenaar Ir. M.F.C. van de Ven Prof. S. Wu 16/12/21» 22/6/212 1

2 Outline Introduction Partial healing model Experimental work Test results and discussion Conclusions 2

3 Introduction Fatigue cracking Rutting Others Raveling Fatigue damage Failure modes on pavement Fatigue cracking 3

4 Introduction Fatigue tests in the lab Simple Flexure: 2-point bending 4-point bending 3-point bending Rotating cantilever Direct Axial Loading: Uniaxial tension and compression with Cylindrical specimen Necked-cylindrical specimen Diametral Loading: Indirect tensile test 4

5 Introduction 4PB test equipments

6 Introduction 4PB test equipments RILEM committee TC 182 PEB N f,5 = α*ε^(-β) 1,E+9 Fatigue life N f,5 1,E+8 1,E+7 1,E+6 1,E+5 T/C 3PB 4PB 2PB T/C: France, Sweden 2PB: France, Belgium 3PB: the Netherlands 4PB: the Nethlands, UK, Poland, Portugal ITT: Sweden 1,E+4 1,E ITT ε (µm/m) N 3PB > N 4PB > N 2PB > N T/C > N ITT 6

7 Introduction Stress-strain distribution Inhomogeneous test Homogenous test Material property 7 Specimen property

8 Introduction Influence factors for stress-strain field 8

9 Partial Healing model Theory [A.C. Pronk 21] Stress Loading Dissipated energy Unloading Strain System loss W syst can be ignored for good equipment Total dissipated energy W tot + Fatigue consumption + Visco-elastic loss Wfat W dis decrease the stiffness and increase the phase angle transformed into heat W sin dis W fat W dis 9

10 Partial Healing model Functions in strain controlled mode Stiffness damage part Q W W sin Ssin fat dis 2 d d Wdis 2 Q Wdis f Ssin dt dt t Describe the evolution of the loss and storage stiffness modulus during the fatigue test for a unit volume Loss modulus Storage modulus t t dq F t Ssin F e d 1 1 d t t dq G t Scos G e d 2 2 d 1 recoverable damage unrecoverable damage

11 Partial Healing model Solutions for UT/C fatigue test Loss modulus Bt sin F t S F e Cosh Ct DSinh Ct Storage modulus G t G F 2 C 2 1 e Bt Sinh Ct Bt 1e Cosh Ct ESinh Ct Model parameters: F, G, α 1, α 2, β *, γ 1, γ 2 11

12 Experimental work Materials percentage passing/% DAC /8 Desired Min Max sieve size/mm Gradation of Dense asphalt concrete (DAC /8) PReSBOX compactor Sieve (mm) Crushed stone Composition of DAC /8 Crushed sand Filler Binder Total Wt. % Road and 7.9 Railway Engineering 6.5 1

13 Experimental work Specimen Size 1.5 Dimensions of specimen Specimen size Length [mm] Width [mm] Height [mm] H/L ratio Size.5 Size 1.

14 Test setup Experimental work φ Strain Stress Test conditions Loading mode Strain-controlled Temperature 2 ºC Frequency 1 Hz Waveform sinusoidal Strain level 5~2 μm/m Size.5 Size 1. Size

15 Test results and discussion Initial stiffness Initial stiffness [MPa] Size.5 Size 1. Size Strain F S sin ; G S cos 15

16 Test results and discussion Evolution of stiffness and phase angle Stiffness Smix Predicted Smix 1 Phase angle φ Predicted φ 4 Stiffness [MPa] Phase angle [deg] Number of cycles Size 1., C-1-9, ε = 1 μm/m 16 α 1 =; α 2 =937; β=68345; γ 1 =21; γ 2 =47

17 Test results and discussion Parameter α 1, α 2 & β* α Size.5 Size1. Size1.5 β [1-5/s] Size1. Size 1 Size 1.5 (1.11 ) * Strain level [μm/m] Strain [μm/m] ; a b; *

18 Test results and discussion PH model parameters γ 1 & γ 2 ; * * 1 1 limit1 2 2 limit 2 Model parameter δγ1,2* γ1_size.5 γ2_size.5 γ1_size 1 γ2_size 1 γ1_size 1.5 γ2_size Strain [μm/m] Specimen size Predicted endurance limit [μm/m] 85~96 91~98 88~94 18

19 Verification Test results and discussion Stiffness [MPa] Complex stiffness Phase angle φ PH model Predicted φ Number of cycles Size1.@155 μm/m Phase angle [ ] Relative error n 1 D m D D D m : measured data D p : predicted data n: total number of data m n p 1% Model parameters F G α 1 α 2 β* γ 1 γ 2 Relative error of S 19 Relative error of φ ε =155 μm/m % 5.28%

20 Test results and discussion Fatigue life definition 12 1 Stiffness Dissipated energy ratio 6 5 Stiffness [MPa] % of the initial stiffness DER 2 1 N R N PH N f, Number of cycles N f,5 : traditional fatigue life N R : determined by dissipated energy ratio N PH : determined by PH model DER i N i1 w w N i

21 Test results and discussion Comparison of fatigue life Number of cycle Size1 NPH NR Nf, Strain level[μm/m] 21

22 Test results and discussion Size effect on fatigue life NPH N PH 1.E+7 1.E+6 1.E+5 Nph_Size.5 Nph_Size1. Nph_Size1.5 Specimen size 1. NPH k k 2.5E+14 b Material coefficient E b R E Strain level [μm/m] E E

23 Conclusions PH model provides a good prediction for the evolution of complex stiffness modulus and phase angle in the uniaxial tension and compression test (UT/C test). The model parameter γ 1 and γ 2 can be used to determine the range of endurance limit, and and this range does not change significantly with the increase of the specimen size. But more tests are needed to validate this. N PH and N R are close to each other compared to the traditional fatigue life N f,5 The fatigue life obtained from the UT/C fatigue test is independent of the specimen size. 23

24 Study in the future Validate of the endurance limit ε limit predicted by the PH model Based on the UT/C test results, apply the PH model to the inhomogeneous fatigue tests, e.g. 4 point bending, 2 point bending fatigue tests, etc. Investigate the influence of temperature, loading mode. 24

25 Thanks for your attention!