ASPHALT MIXTURE FATIGUE TESTING
Influence of Test Type and Specimen Size
ASPHALT MIXTURE FATIGUE TESTING
Influence of Test Type and Specimen Size
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op maandag 18 november 2013 om 10:00 uur
door Ning LI
Master of Science in Material Science and Engineering Wuhan University of Technology, P.R. China
Prof. S.P. Wu, BSc., MSc., PhD. Copromotor
Ir. M.F.C. van de Ven
Samenstelling promotiecommissie:
Rector Magnificus, Technische Universiteit Delft, voorzitter Prof. dr. ir. A.A.A. Molenaar Technische Universiteit Delft, promotor Prof. S.P. Wu, BSc., MSc., PhD. Wuhan University of Technology, promotor Ir. M.F.C. van de Ven Technische Universiteit Delft, copromotor Prof. dr. ir. S.M.J.G. Erkens Technische Universiteit Delft
Prof. dr. A. Scarpas Technische Universiteit Delft Prof. dr. ir. H.E.J.G. Schlangen Technische Universiteit Delft Dr. A. Vanelstraete Belgian Road Research Centre
Published and distributed by: Ning Li
Road and Railway Engineering Section Faculty of Civil Engineering and Geosciences Delft University of Technology
P.O. Box 5048, 2600 GA Delft, the Netherlands
E-mail: lining-008@hotmail.com, lining0618@gmail.com ISBN: 978-94-6186-235-8
Key words: Fatigue Test; Endurance Limit; Test Type; Specimen Size; Yield Surface; Safety Factor
Printing: Wohrman Print Service, Zutphen (the Netherlands)
©2013 by Ning Li
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the proprietor.
i
Looking back to the starting point is helpful for moving forward in a right way. Life is not easy, especial for a PhD student living in a foreign country. During the five years’ study in Delft, many people gave me their guidance, encouragement and support when I faced difficulties. Without their efforts, this research would never have been completed. Therefore, this moment is a good opportunity for me to express my sincere gratitude to all of them.
This PhD project was originated from the cooperation between the Delft University of Technology (TUD) and Wuhan University of Technology (WHUT). The research presented in this dissertation was carried out in the Road and Railway Engineering Section of the Faculty of Civil Engineering and Geosciences at the TUD. Firstly, the appreciation goes to those who built up the cooperative link between TUD and WHUT. The author also would like to thank the financial supports from the China Scholarship Council (CSC) and the TUD.
I would like to express my deepest appreciation to my promoter, Prof.dr.ir. A.A.A. Molenaar. He always provided me with the valuable guidance and encouragement throughout every stage of my PhD study. I enjoyed the great benefit from not only his academic attainments but also his wisdom of life. His tireless efforts and constructive comments on this dissertation are highly appreciated. At the same time, sincere gratitude goes to my promoter Prof. Shaopeng Wu, who supervised my bachelor, master and PhD study. He advised me to start my PhD study abroad and let me expand my field of vision. His professional knowledge and experience in road industry led me into the road engineering field.
I am grateful for my daily supervisors Associate Professor Martin van de Ven. He always gave his patient guidance whenever I need. His careful review on my papers, reports and dissertation are deeply appreciated. I would like to extend my sincere gratitude to Ir. A.C. Pronk for his contribution on the calibration and the modeling work in this research. Under his guidance, I adapted myself to the new study environment quickly and did not feel fear of those complex equations. Even after his retirement, he still came over and discussed with me when I need help. Thanks so much for all your efforts. My sincere appreciation goes to Prof.dr. R.L. Lytton for his arrangement and guidance when I was doing the project in Texas A&M University. Also many thanks to Dr. Rong Luo for her kind help during my stay in Texas. I would like to appreciate Prof. Halil Ceylan from Iowa State University. His valuable suggestions on the data analysis are highly acknowledged. I also would like to thank Dr. Milliyon Woldekidan for the valuable discussion and kind help with the finite element analysis.
I would like to thank all the colleges and former colleges of Road and Railway Engineering Section. The extensive laboratory work could not have been successfully finished without the arrangement and support provided by Associate professor Lambert Houben, Abdol Miradi, Marco Poot, Jan-Willem Bientjes, Jan Moraal and Dirk Doedens.
ii
Barnhoorn and Sonja van de Bos for their kind help with the daily administration affaires. I would like to thank Prof. Tom Scarpas, Prof. Sandra Erkens, Prof. Rolf Dollevoet, Dr. Rien Huurman, Accociate Professor Zili Li and Dr. Xueyan Liu. Their support and guidance are deeply appreciated. Many thanks to all the PhD students, liantong Mo, Jian Qiu, Gang Liu, Xin Zhao, Eyassu, Alemgena Araya, Yue Xiao, Jingang, Sadegh, Mohamad, Oscar, Marija, Maider, Shaoguang, Nico, Dongya, Pengpeng, Chang, Haoyu, Lizuo, Xiangyun and all the new PhD students. I really enjoy the time here with all of them. Special thank goes to my officemates Diederik van Lent, Yuan Zhang and former officemate Dongxing. I feel fortunate that I have sit in the Room 1.29 for 5 years. I will never forget the moments when we were talking about our different cultures and languages, when we were sharing our knowledge and experiences and when we were playing table tennis.
I appreciate the wonderful time that I have spent together with all my friends: Associate Prof. Ye, Xu Jiang, Xuhong Qiang, Quantao Liu, Hailing Zhang, Xuming Shan, Ying Wang, Juan Tong, Lili Wu, Huanhuan Mao, Nannan Li, Lin Liu, Huisu Chen, Zhiwei Qian, Yuguang Yang, Qi Zhang, Jinlong Li, Haoliang Huang, Bei Wu, Jiayi Chen, Yun Zhang, Yong Zhang, Yuan Qiu, etc. Thanks all of them for giving me kind help and enjoyable time.
Finally, my deepest gratitude goes to my family for their endless love and continues support. My parents have never complained how less time I have spent with them since I left home for my study. I appreciate their encouragement and understanding. My special thanks to my wife Zhuqing Yu for her continuous support, patience and optimistic attitude. No matter what happen, she always stand firm behind me and take good care of my life even when she was also busy with her PhD study. This dissertation is dedicated to my family.
Ning Li
李宁
iii
Fatigue characterization of an asphalt mixture is commonly estimated by laboratory fatigue tests. Based on the classical fatigue analysis, fatigue lives obtained from different test devices are not comparable even when they are performed at the same test conditions. It is believed that there are two main reasons causing the difference in fatigue results being the difference in stress-strain distribution of the different specimens and the fatigue analysis approach. This research focuses on the harmonization of the fatigue results obtained from the different methods, which are recommended by the European standard EN 12697-24. The main goal is to find a correlation between the different fatigue test methods and to improve the classical fatigue analysis approach to better represent the actual fatigue characteristics of asphalt mixtures.
To realize the main objective of the study, an extensive fatigue testing program was carried out on dense asphalt concrete 0/8 (DAC 0/8). In the program, uniaxial tension and compression (UT/C) fatigue tests, four-point bending (4PB) fatigue tests and indirect tensile (IT) fatigue tests were performed. For each fatigue test, specimens with different sizes were tested to explore the size effect on the fatigue results. In order to limit the test program, the tests were performed in two loading modes, at two temperatures and one frequency.
For the 4PB fatigue test, the measured displacement highly depends on the properties of the loading frame. Calibration tests on the 4PB test setup were conducted to obtain the pure bending deflection of the beam.
Comparison of the fatigue results obtained with the different test methods at the same test condition and loading mode shows that the fatigue life from the 4PB test is the longest and from the IT test is the shortest. Because of the homogeneous tensile strain field, the UT/C and IT fatigue results are not significantly influenced by the specimen size. However, the 4PB test results depend on the dimension of the used specimen, because the stress-strain field of the beam specimen varies along the length and cross section.
The partial healing (PH) model was used to determine the relationship between the UT/C and 4PB fatigue results in strain-controlled mode. It is a material model that describes the evolutions of the stiffness and phase angle for a unit volume during testing. This implies that the model can be directly applied to the fatigue results obtained from the “homogenous” tests, the UT/C test, because the strain is uniformly distributed throughout the specimen. When analyzing the 4PB results, the backcalculated stiffness is not the local stiffness of the material but the so-called weighted overall stiffness of the whole specimen. Therefore a weighing procedure is required to calculate the weighted overall stiffness modulus from the local stiffness by taking into account the dimensions and the strain distribution of the specimen. By adjusting the model parameters, the PH model provides a good simulation for the evolutions of the stiffness and phase angle. All the model parameters can be expressed as functions of the applied strain level. The trends of the parameter δγ1 and δγ2 indicate the existence of an endurance limit. The predicted
iv
test, the local stiffness at different parts of the beam can be calculated by means of the PH model. The evolution of the calculated stiffness at the surface in the midsection of the beam is comparable with the UT/C fatigue results when the pure bending strain on the beam surface is equal to the tensile strain in the cylinder. Therefore the PH model offers a possibility to compare different fatigue results.
In the second part of this research, the yield surface concept was applied to develop a new fatigue analysis approach. As a visco-elastic material, the yield surface of an asphalt mixture highly depends on temperature and strain rate. Therefore, monotonic uniaxial compression (MUC) and monotonic uniaxial tension (MUT) tests were performed at different temperatures and strain rates to derive such yield surfaces. For the three fatigue tests, the yield surface at the critical location of the specimen was determined in the I1-√J2
space. The fatigue results were then interpreted by comparing the actual stress condition with the yield surface.
A new parameter R∆ was introduced as an indicator of the “safety against failure”. By
comparing the R∆ values at the different locations of the specimen for the IT test, the
weakest points are found at the locations with the maximum horizontal tensile strain, which are close to the loading strips, instead of the center of the specimen. A straight line was found by plotting R∆ at the critical location and the fatigue life on a log-log scale.
Compared to the traditional fatigue analysis, the size effect on the fatigue results was excluded by using this new fatigue relation. For the stress-controlled mode, the fatigue lines obtained from the UT/C test show a good agreement with the IT fatigue results. Of course the influence of temperature and loading mode still exists in this new fatigue method. In the normal coordinate, when the fatigue life tends to infinity, R∆ becomes a
constant value, denoted by Rlimit. The parameter Rlimit represents the endurance limit in a
three-dimensional state. This value does not change with specimen size and test type but is influenced by the temperature and loading mode.
Based on all the test results and their analysis in this research, it was concluded that the UT/C fatigue results are material properties and not influenced by specimen size. The PH model provides a good simulation of fatigue behavior of the asphalt mixture and is able to find the correlation between the UT/C and 4PB test results. The developed fatigue analysis approach characterizes the fatigue performance of asphalt mixtures in three-dimensional state, which is more close to the field situation. The endurance limit predicted by the new fatigue approach is independent of the specimen size and fatigue test type.
v
Het vermoeiingsgedrag van asfaltmengsels wordt in het algemeen bepaald door middel van vermoeiingsproeven in het laboratorium. Wanneer de klassieke vermoeiingsanalyse wordt gebruikt, zijn vermoeiingslevensduren verkregen met verschillende test types niet vergelijkbaar, zelfs niet wanneer zij worden uitgevoerd bij dezelfde proefomstandigheden. Aangenomen wordt dat er twee belangrijke oorzaken zijn voor het verschil in vermoeiingsresultaten, namelijk het verschil in spanning-rek verdeling in de verschillende proef types en de manier waaropn de analyse van de resultaten wordt uitgevoerd. Dit onderzoek richt zich op de harmonisatie van de vermoeiings resultaten van een aantal methoden die worden aanbevolen door de Europese norm EN 12697-24. Het belangrijkste doel is om een correlatie tussen de verschillende vermoeiingsproeven te vinden en de klassieke vermoeiingsanalyse te verbeteren teneinde de werkelijke vermoeiingseigenschappen van asfaltmengsels zo goed mogelijk te kunnen bepalen. Om het hoofddoel van de studie te realiseren is een uitgebreid vermoeiingsonderzoek uitgevoerd op dicht asfaltbeton 0/8 (DAC 0/8). In het onderzoeksprogramma zijn uniaxiale trek/druk vermoeiingsproeven (UT/C), vierpuntsbuigingsproeven (4PB) en indirecte trekproeven (IT) uitgevoerd. Voor elk proeftype zijn proefstukken met verschillende afmetingen getest om het effect van de afmetingen op de vermoeiingsresultaten te onderzoeken. Om het testprogramma te beperken, zijn de proeven uitgevoerd met twee verschillende belastingswijzen (constante spanning en constante rek), bij twee temperaturen en met één frequentie.
Voor de 4PB vermoeiingsproef is de gemeten verplaatsing sterk afhankelijk van de eigenschappen van het frame van de proeftopstelling. Om deze reden zijn kalibratieproeven op de 4PB opstelling uitgevoerd om de zuivere doorbuiging van de balk te kunnen bepalen.
Bij dezelfde proefomstandigheden en belastingwijze, is de vermoeiingslevensduur in de 4PB proef het langste en die in de IT-test de kortste. Vanwege het homogene trekspanningsveld worden de UT/C en IT vermoeiingsresultaten niet significant beïnvloed door de afmetingen van de proefstukken. Echter, de 4PB resultaten zijn wel afhankelijk van de hoogte van de gebruikte balk, omdat het spanning-rekgebied in de balk varieert over de lengte- en dwarsdoorsnede.
Het partial healing (PH) model is gebruikt om de relatie tussen de UT/C en 4PB vermoeiingsresultaten met constante rek te bepalen. Het is een materiaalmodel dat de ontwikkeling van de stijfheid en fasehoek van een volume-eenheid tijdens de vermoeiingsproef beschrijft. Dit impliceert dat het model direct toepasbaar is op de vermoeiingsresultaten van de "homogene" proeven, zoals de UT/C -test, omdat de rek gelijkmatig over het gehele proefstuk verdeeld is. Bij het analyseren van de 4PB resultaten, is de uit de maximale doorbuiging van de balk teruggerekende stijfheid niet de werkelijke stijfheid van het materiaal, maar een gewogen stijfheid van het gehele proefstuk. De werkelijke stijfheid van het materiaal varieert nl over de lengte en de
vi
de afmetingen en de rekdistributie in het proefstuk. Door het aanpassen van de modelparameters, kan met het PH-model de ontwikkeling van de stijfheid en fasehoek worden gesimuleerd. Alle modelparameters kunnen worden uitgedrukt als functie van de aangebrachte rekniveaus. De trends van de parameters δγ1 en δγ2 wijzen op het bestaan
van een vermoeiingsgrens. De voorspelde vermoeiingsgrens voor de UT/C proeven is ongeveer 68 µm / m voor het geteste DAC 0/8 mengsel, en deze blijkt onafhankelijk te zijn van de afmetingen van het proefstuk en de temperatuur. Voor de 4PB proeven kan de ontwikkeling van de lokale stijfheid op iedere plaats in het proefstuk worden berekend met behulp van het PH model. De ontwikkeling van de lokaal berekende stijfheid aan het oppervlak in het middelste gedeelte van de balk is vergelijkbaar met de UT/C vermoeiingsresultaten wanneer de zuivere buigingsrek aan het oppervlak van de balk gelijk is aan de trekrek in de cilinder. Hiermeebiedt het PH-model de mogelijkheid om de vermoeiingsresultaten van verschillende types proeven met elkaar te vergelijken.
In het tweede deel van dit onderzoek is het yield surface concept toegepast bij de analyse van de vermoeiingsresultaten. Voor een visco-elastisch materiaal zoals een asfaltmengsel, is de yield surface sterk afhankelijk van de temperatuur en de reksnelheid. Om deze reden zijn monotone uniaxiale druk- (MUC) en monotone uniaxiale trek (MUT) proeven uitgevoerd bij verschillende temperaturen en reksnelheden om de contouren van de yield surface te bepalen. Voor de drie types vermoeiingsproeven zijn de kritieke locaties van het proefstuk bepaald in de zogenaamde I1-√J2 ruimte. De vermoeiingsresultaten zijn
vervolgens geïnterpreteerd door de werkelijke spanningstoestand te vergelijken met de driedimensionale yield surface voor de diverse proeftypes.
Een nieuwe parameter R∆ isgeïntroduceerd als indicator van de "veiligheid tegen
bezwijken". Door de R∆ waarden te vergelijken die voor verschillende locaties in het IT
proefstukr zijn berekend zijn de locaties gevonden waar falen het eerst op zal treden. Deze bevinden zich dichtbij de belastingstrippen, in plaats van in het midden van het proefstuk. Op log-log schaal is een rechte lijn gevonden bij het plotten van R∆ op de
kritieke locatie en de vermoeiingslevensduur. Vergeleken met de traditionele vermoeiingsanalyse, ishet effect van de afmetingen op de vermoeiingsresultaten geëlimineerd bij gebruik van deze nieuwe vermoeiingsrelatie. Voor de spanningsgestuurde proef laten de vermoeiingslijnen verkregen uit de UT/C -proef een goede overeenkomst zien met de IT vermoeiingsresultaten. Maar de invloed van de temperatuur en belastingswijze blijft aanwezig, ook in deze nieuwe analysemethode. Wanneer de vermoeiingslevensduur naar oneindig gaat blijkt R∆ een constante waarde
aan te nemen, die aangeduid is met Rlimit. De parameter Rlimit vertegenwoordigt de
endurance limit in de driedimensionale toestand. Deze waarde verandert niet met proefstukrgrootte en type proef, maar wordt wel beïnvloed door de temperatuur en belastingswijze.
Op basis van alle resultaten en hun analyse in dit onderzoek kan worden geconcludeerd dat de eigenschappen zoals bepaald met de UT/C proef "echte" materiaaleigenschappen zijn die niet beïnvloed worden door de proefstukafmetingen. Het PH model simuleert het
vii
maakt het mogelijk de vermoeiingsprestaties van asfaltmengsels in een driedimensionale spanningstoestand te bepalen, vergelijkbaar met die welke in de praktijk optreden. De endurance limit die wordt voorspeld met de nieuwe vermoeiingsaanpak is onafhankelijk van de afmetingen van het proefstuk en het type vermoeiingsproef.
ix
HMA Hot Mix Asphalt
2PB Two-Point Bending
3PB Three-Point Bending
4PB Four-Point Bending
ITFT Indirect Tensile Fatigue Test NAT Nottingham Asphalt Tester
UT/C Uniaxial Tension and Compression
IT Indirect Tension
S-N Stress amplitude-Life
AC Asphalt Concrete
TRRL Transport and Road Research Laboratory CEN European Committee for Standardization
PI Penetration Index
CF Correction Factor
ER Energy Ratio
RDEC Ratio of Dissipated Energy Change
PV Plateau Value
GAC Gravel Asphalt Concrete
PH Partial Healing
2D Two-Dimensional
3D Three-Dimensional
ACRe Asphalt Concrete Response
DAC Dense Asphalt Concrete
SA Sand Asphalt
CDAS Control Data Acquisition System UTM Universal Testing Machine FFT Fast Fourier Transform
LVDT Linear Variable Differential Transformer CDAS Control and Data Acquisition System WLF Williams-Landel-Ferry
DER Dissipated Energy Ratio
MUC Monotonic Uniaxial Compression MUT Monotonic Uniaxial Tension
EME Enrobé á Modele Elevé
SMA Stone Mastic Asphalt
GAC Gravel Asphalt Concrete
MPRE Mean Percent Relative Error l.o.c. Level of Confidence
HISS Hierarchical Single Surface
FEM Finite Element Modelling
GUI Graphical User Interface ABAQUS A Finite Element Package
x
ASTM American Society for Testing and Materials
AASHTO American Association of State Highway and Transportation Officials RILEM International Union of Laboratories and Experts in Construction Materials
xi Acknowledgements ... i Summary... iii Samenvatting ... v List of Abbreviations ... ix Chapter 1 Introduction... 1
1.1 Fatigue Damage in Asphalt Pavements ... 1
1.2 Fatigue Failure Mechanism... 2
1.3 Evaluation of Fatigue Properties... 3
1.4 Problem Statement and Objectives ... 4
1.5 Organization of the Dissertation ... 6
References... 8
Chapter 2 Literature Review ... 11
2.1 Background of Fatigue Research on Asphalt Mixtures ... 11
2.2 Laboratory Fatigue Test Methods ... 12
2.2.1 Simple Flexure Test ... 12
2.2.1.1 Two-Point Bending (2PB) Test ... 12
2.2.1.2 Three-Point Bending Test ... 13
2.2.1.3 Four-Point Bending Test... 14
2.2.1.4 Rotating Bending Test ... 15
2.2.2 Direct Axial Loading Test ... 16
2.2.3 Diametral Loading Test (Indirect Tensile Test)... 17
2.3 Influence of Test Type, Specimen Size and Test Conditions on Fatigue Results ... 18
2.3.1 Influence of Test Type and Specimen Size... 19
2.3.1.1 Influence of Test Type ... 19
2.3.1.2 Influence of Specimen Size ... 21
2.3.2 Influence of Loading Mode ... 22
2.4 Fatigue Analysis Approach... 26
2.4.1 Results of Laboratory Fatigue Tests ... 26
2.4.2 Classical Fatigue Analysis ... 29
2.4.3 Dissipated Energy Approach ... 34
2.4.3.1 Dissipated Energy Theory... 34
2.4.3.2 Cumulative Dissipated Energy ... 35
2.4.3.3 Dissipated Energy Ratio ... 37
2.4.4 Fracture Mechanics Approach ... 41
2.4.4.1 Theory ... 41
xii
2.5.2 Weibull’s Theory ... 47
2.5.2.1 Survival Probability ... 47
2.5.2.2 Calculation of Survival Probability ... 48
2.5.2.3 Application in Fatigue Test... 50
2.5.3 Mechanical Damage Model ... 52
2.5.3.1 Theory ... 52
2.5.3.2 Size Effect of the Damage Model ... 53
2.5.3.3 Comparison between Model and Experiments ... 54
2.6 Summary ... 55
References... 56
Chapter 3 Research Methodology ... 65
3.1 Introduction... 65
3.2 Research Methodology ... 66
References... 68
Chapter 4 Mixture Design and Specimen Preparation ... 69
4.1 Selection of the Mixture... 69
4.2 Mixture Design ... 71
4.2.1 Materials ... 71
4.2.2 Mixture Design ... 72
4.3 Specimen Preparation ... 74
4.3.1 Mixture Compaction ... 74
4.3.2 Selection of Specimen Size... 76
4.3.3 Specimen Preparation ... 77
References... 82
Chapter 5 Different Laboratory Fatigue Experiments... 83
5.1 Introduction... 83
5.2 Test Equipment ... 83
5.2.1 Uniaxial Tension and Compression (UT/C) Test ... 83
5.2.2 Four-Point Bending (4PB) Test ... 84
5.2.3 Indirect Tensile (IT) Fatigue Test ... 90
5.3 Calibration of the 4PB Test Equipment ... 90
5.3.1 Theory ... 91
5.3.2 Test Program ... 93
5.4 Complex Modulus and Fatigue Tests ... 96
5.4.1 Complex Modulus Test... 96
5.4.2 Fatigue Test... 97
5.5 Data Processing... 98
5.5.1 UT/C Test... 98
5.5.2 4PB Test... 99
xiii
5.6.2 Fatigue Test Results... 108
5.7 Summary ... 130
5.7.1 Test Setup... 130
5.7.2 Test Results... 131
References... 132
Chapter 6 Application of Partial Healing Model on Strain Controlled Fatigue Tests ... 133
6.1 Introduction... 133
6.2 Application of PH Model on UT/C Test Results ... 133
6.2.1 PH Model Theory ... 133
6.2.2 Determination of PH Model Parameters... 139
6.3 Application of PH Model on 4PB Test Results ... 144
6.3.1 Weighing Procedure for 4PB Test ... 144
6.3.2 Determination of PH Model Parameters... 148
6.4 Correlation between UT/C and 4PB Fatigue Test Results ... 153
6.5 Conclusions... 155
References... 157
Chapter 7 Monotonic Uniaxial Tension and Compression Tests ... 159
7.1 Introduction... 159
7.2 Test Equipment ... 159
7.2.1 Monotonic Uniaxial Compression Test ... 159
7.2.2 Monotonic Uniaxial Tension Test ... 161
7.3 Test Condition... 162
7.3.1 Central Composition Rotatable Design ... 162
7.3.2 Test Conditions for MUC and MUT Tests ... 163
7.4 Test Procedure ... 164
7.4.1 Test Procedure for MUC Tests ... 164
7.4.2 Test Procedure for MUT Tests ... 165
7.5 Data Processing... 166
7.5.1 Stress and Strain... 166
7.5.2 Strain Rate, Maximum Stress, Tangent Stiffness and Onset of Dilation168 7.6 Test Results... 169
7.6.1 MUC Test Results... 169
7.6.2 MUT Test Results ... 175
7.7 The Unified Model... 177
7.8 Prediction of the Unified Model Parameters ... 180
7.9 Conclusions... 195
xiv
8.2 Material Model Concept ... 197
8.3 Determination of Model Parameters ... 202
8.3.1 Model Parameters R and γ ... 202
8.3.2 Model Parameter n ... 205
8.3.3 Model Parameter α... 205
8.3.4 Determination of Yield Surface ... 207
8.4 Critical Location ... 209
8.5 Determination of Yield Surface for Fatigue Test ... 212
8.6 Relationship between R∆ and Fatigue Life ... 215
8.7 Conclusions... 225
References... 226
Chapter 9 Conclusions and Recommendations... 227
9.1 Conclusions... 227
9.1.1 Conclusions Related to Literature Review ... 227
9.1.2 Conclusions Related to Fatigue Test Equipment ... 227
9.1.3 Conclusions Related to Stiffness and Fatigue Results... 228
9.1.4 Conclusions Related to Partial Healing Model ... 228
9.1.5 Conclusions Related to Monotonic Test Results ... 229
9.1.6 Conclusions Related to Yield Surface Approach... 230
9.2 Recommendations... 230
9.2.1 Recommendations Related to Experimental Work... 230
9.2.2 Recommendations Related to Partial Healing Model ... 231
9.2.3 Recommendations Related to Yield Surface Approach... 231
Appendix A Calculations for 4-Point Bending Test... 233
1
Chapter 1 Introduction
1.1 Fatigue Damage in Asphalt Pavements
Fatigue is defined as the phenomenon of deterioration of a material (reduction in stiffness and strength, ending in fracture) under repeated loading. Similar to other materials, the stiffness and strength of asphalt concrete decrease when it is subjected to repetitive loading [Pell, 1962].
Because of its cost efficiency, reduction in traffic noise, improved safety and comfort and so on, asphalt concrete has been widely used in pavement structures since the beginning of the last century [Hveem and Davis, 1950] [Hindley, 1971]. With the increase of traffic volume and weight, fatigue cracking of the bituminous layer has become one of the major distress modes in flexible road pavements associated with repeated traffic loads. Fatigue cracks decrease the structural capacity of the pavement and increase the maintenance cost. Furthermore, once fatigue cracks propagate through the entire asphalt thickness, water and aggressive agents can infiltrate into the unbound layers, which greatly accelerates the deterioration process. Therefore, understanding the fatigue cracking phenomenon and measuring the fatigue properties of asphalt concrete is essential for the design of flexible pavements. Figure 1-1 shows some examples of fatigue failure in pavements.
Figure 1-1 Fatigue cracks at the surface of asphalt pavement
Fatigue cracking is associated with repetitive traffic loading and pavement thickness [Roberts et al., 1996] [McGennis et al., 1994]. Traditionally, it is believed that cracking initiates at the bottom of the hot mix asphalt (HMA) layers where the tensile stress is the highest, then migrates upward toward the surface where it shows up as one or more longitudinal cracks. This is commonly referred to as "bottom-up" or "classical" fatigue cracking. Researchers however found that in thick pavements (≥160 mm), the cracks most likely initiate from the top in areas of high localized tensile stresses resulting from tire-pavement interaction and asphalt binder aging. They then propagate down to a depth of approximately 50 mm; this is called top-down cracking [Molenaar, 1983] [Gerritsen, 1987] [Molenaar, 2004] [Uhlmeyer, 2000]. Up till now, the mechanism of initiation and progression of top-down cracks is not thoroughly understood. It is commonly assumed that high concentration of stresses at the tire-pavement contact surface is the major cause for these cracks.
2
1.2 Fatigue Failure Mechanism
In order to have a better understanding of the fatigue cracking mechanism in asphalt pavements, it is necessary to look at how the wheel load is applied to a pavement structure. Figure 1-2 shows the stress states developed in a particular element of the pavement structure when subjected to a moving wheel load.
Figure 1-2 Stresses induced by a moving wheel load on a pavement element [Brown, 1978]
The moving wheel causes vertical, horizontal and shear stresses on an element underneath the wheel. As a result of the passing wheel load, the vertical compressive stress changes following a half sine wave, but in horizontal direction the element is subjected to a tensile or compressive stress alternatively. The bottom-up cracking is mainly caused by the horizontal tensile stress at the bottom of the asphalt layer. Being a visco-elastic material, the properties of asphalt mixtures are time dependent which will have an effect on the magnitude of the tensile strains developed in the structure. The loading time depends on vehicle speed and the depth below the pavement surface [Collop, 1995]. For example, at a velocity of 60 km/h, the loading time will be approximately 0.015 s at a depth of 150 mm. In addition to the loading frequency, environmental conditions, engineering properties of the asphalt concrete, the condition of underlying layers, and the pavement structure are all contributing factors to fatigue cracking.
Roads do not crack immediately after traffic starts to use the pavement. It usually takes years or millions of load applications from vehicle tires. The sustained traffic loading results in a decrease in the structural strength of the pavement. If the tensile stress exceeds the local tensile capacity of the material, eventually cracking will occur. In the beginning, cracking manifests itself as a series of parallel longitudinal cracks (cracks along the direction of the flow of traffic) in the top layer of the asphalt pavement. These cracks are initially thin and sparsely distributed. If further deterioration continues, these
Stress Moving Wheel Load
Pavement Structure Typical Element Horizontal Stress Shear Stress Vertical Stress Shear Stress Horizontal Stress (compressive) Horizontal Stress (tensile at the bottom of stiff layer)
Vertical Stress (compressive)
Time
3
longitudinal cracks are connected by transverse cracks forming many sided, sharp-angled pieces. This interlaced cracking pattern resembles chicken wire or the skin of an alligator. Figure 1-3 shows examples of the different levels of severity for fatigue cracking.
Figure 1-3 Alligator crack patterns of differing severity [Miller, 2003]
1.3 Evaluation of Fatigue Properties
The fatigue properties of asphalt mixtures are important parameters in pavement design. In order to determine the fatigue resistance of asphalt mixtures, various fatigue tests are carried out in the laboratory at the stress levels, loading times, rest periods and temperature and moisture conditions as realistic as possible. Then the fatigue characteristics of an asphalt mixture derived from the laboratory tests are used as input in the design analysis to predict field performance.
Figure 1-4 Schematic demonstrating the main configurations of fatigue tests [Read, 1996] (a) two point bending; (b) four point bending; (c) three point bending; (d) rotating
bending; (e) direct axial loading; (f) direct axial loading (necked specimen); (g) diametral loading
4
Fatigue tests for asphalt mixtures were developed as early as the fifties of the last century, and different test configurations have emerged since that time. According to the mode of loading the most commonly used tests are classified as simple flexural tests (rotating cantilever, 2-, 3- and 4-point bending), direct axial loading test and diametral loading test [Read, 1996] [Tangella, 1990]. Figure 1-4 gives a schematic representation of the different fatigue tests. The arrows in the figure indicate the direction of the applied loading. A detailed description of each fatigue test will be given in the literature review. During fatigue testing, the specimen is subjected to a repeated load at a certain temperature and frequency. In the classical fatigue analysis, fatigue failure is determined based on the stiffness reduction. For the strain-controlled mode, the failure point is defined as the moment at which the stiffness of the specimen has reduced to 50% of its initial value. For the stress-controlled mode, the failure point is defined as the moment when the specimen has completely fractured. The results of fatigue tests can be interpreted in terms of a relationship between the stress or strain and the number of cycles to failure, which is represented by means of a straight line in a double logarithmic coordinate system [Pell, 1962].
b f
N
= ⋅
k δ
− (1-1)where: Nf : number of cycles to failure;
δ : applied strain level [µm/m] or stress level [MPa];
k and b : coefficients related to the material properties.
1.4 Problem Statement and Objectives
As mentioned in Section 1.3, various fatigue test devices are currently used to evaluate the fatigue performance of asphalt concrete. The two-point bending (2PB) test with trapezoidal specimens was adopted by researchers from Shell [van Dijk, 1975] and LCPC [Bonnot, 1986]. The Shell Laboratory at Amsterdam also has used the three-point bending loading equipment to estimate the fatigue life [van Dijk, 1975]. In the USA [SHRP, 1992] and the Netherlands [Pronk, 1996], the four-point bending test (4PBT) is specified. In the UK and Sweden, the standard fatigue test is the indirect tensile fatigue test (ITFT). The Nottingham Asphalt Tester (NAT) was specially designed for this test [Brown, 1995]. In European standard [EN 12697-24], three bending tests and the indirect tensile test are allowed as the standard fatigue test methods. Inevitably, they all give different results for the same material. Di Benedetto et al. reported an inter-laboratory investigation organized by the RILEM 182-PEB Technical Committee [Di Benedetto, 2004]. More than 150 fatigue tests were carried out using eleven different types of test equipment, including uniaxial tension/compression (UT/C), bending and indirect-tension tests. The classic fatigue relations obtained from the different fatigue tests are shown in Figure 1-5.
5
Figure 1-5 Classic fatigue relations obtained from the different fatigue tests [Di Benedetto, 2004]
Fatigue results are very sensitive to load conditions and the used test type. The Indirect Tension Test (ITT) shows the shortest fatigue life due to accumulation of permanent deformation in addition to fatigue damage. For a given strain amplitude, the beam tests generally result in longer fatigue life compared to T/C (Tension/Compression) tests. The conclusion was that fatigue test results obtained from different test equipment are not comparable to each other. It is therefore desirable to find a way to harmonize the fatigue results obtained from the different test methods and improve the classic fatigue analysis approach to better represent the actual fatigue characteristics of an asphalt mixture. In order to achieve these goals, the following objectives were defined in this research: (1) Compare the fatigue results obtained from representative fatigue test methods and
analyze their failure mechanisms.
(2) Explore the influence of the specimen size on fatigue results. Three different sizes (size 0.5, 1.0 and 1.5) are selected in this research, in which size 1.0 corresponds to the standardized size. Size 0.5 is a smaller one, a half of the size 1.0 and size 2 is twice larger than the standardized size.
(3) Develop a material model which is able to describe the fatigue behavior obtained from the different fatigue tests.
(4) Develop a new fatigue analysis approach to decrease if possible exclude the influence of the test type and specimen size on the fatigue result.
80 1,E+09 1,E+08 1,E+07 1,E+06 1,E+05 1,E+04 1,E+03 100 110 ε 0 (µm/m) Nf50 3PB 4PB 2PB T/C ITT Nf50 = α*ε^(-β)
6
1.5 Organization of the Dissertation
This thesis consists of nine chapters. Chapter 1 gives a general introduction of the fatigue failure of asphalt pavements and the assessment of the fatigue characteristics in the laboratory. Problem statements and objectives are described.
Chapter 2 provides a literature review on laboratory fatigue test methods and fatigue analysis models.
In Chapter 3, the research methodology is presented.
Chapter 4 gives a detailed description of the materials used in this study. Ample attention is given to the mixture design and specimen preparation.
Chapter 5 describes the experimental work. Three different fatigue configurations, uniaxial tension and compression test, four-point bending test and indirect tension test, were conducted with different specimen sizes. The results of the fatigue tests and the interpretation techniques are also discussed.
In Chapter 6, the Partial Healing model is applied to simulate the evolution of the complex modulus and the phase angle for the uniaxial tension and compression and the four-point bending fatigue tests in strain controlled mode.
In Chapter 7, the results of the monotonic uniaxial tension and compression test are given at different strain rates and temperatures. In order to determine the yield surface, the unified model is used to calculate the strength and failure strain in both compression and tension.
Chapter 8 describes the yield surface concept and its application on the fatigue results. A new parameter R∆ is introduced as safety factor and a new fatigue analysis approach is
developed to reduce or exclude the influence of the test type and specimen size on the fatigue life.
7
Figure 1-6 Structure of the dissertation
Chapter 3 Research Methodology Chapter 2 Literature Review
Chapter 1 Introduction
Chapter 4 Mixture Design and Specimen Preparation
Chapter 5 Different Laboratory Fatigue Experiments
Chapter 6 Application of Partial Healing Model on Strain Controlled Fatigue Tests
Chapter 7 Monotonic Uniaxial Tension and Compression Test
Chapter 8 Yield Surface and Fatigue Tests
Chapter 9 Conclusions and Recommendations
8
References
Bonnot, J., Asphalt aggregate mixtures, Transportation Research Record 1096, Transportation Research Board, 1986, pp.42-50.
Brown, S.F., Practical test procedures for mechanical properties of bituminous materials, Proceeding of ICE Transport 111, 1995, pp. 298-297.
Collop, A.C, Cebon, D., A theoretical analysis of fatigue cracking in flexible pavements, J. Mech. Eng. Sci., IMech E, 1995, Vol 209, No C5, pp. 345-361.
Di Benedetto H., de la Roche C., Baaj H., Pronk A., Fatigue of bituminous mixtures. Materials and Structures, 2004, vol. 37, n. 3, pp. 202-216.
European committee for standardization, Bituminous Mixtures-Test Methods for Hot Mix Asphalt, BS EN 12697: Part 24: Resistance to Fatigue. CEN, Brussels, 2004.
Gerritsen, A.H.; van Gurp, C.A.P.M.; van der Heide, J.P.J.; Molenaar, A.A.A. and Pronk, A.C., Prediction and Prevention of Surface Cracking in Asphaltic Pavements. Proceedings, 6th International Conference Structural Design of Asphalt Pavements, The University of Michigan. Ann Arbor, Michigan, July 1987, pp. 378-391. Hindley, G., A History of Roads, the Chausser Press Ltd., Bungay, Suffolk, ISBN 432-06-7361, 1971.
Hveem, F. and Davis, H., Some Concepts Concerning Triaxial Compression Testing of Asphalt Paving Mixtures and Subgrade Materials, ASTM Special Technical Publication No. 106: Triaxial Testing of Soils and Bituminous Mixtures, American society for Testing Materials (ASTM), 1916 Race Street, Philadelphia, 1950.
McGennis R.B., Anderson R.M., Kennedy T.W., Solaimanian M., Background of Superpave Asphalt Mixture Design and Analysis.Publication, No.FHWA-SA-95-003, 1994.
Miller, J.S., Bellinger, W.Y., Distress Identification Manual for the Long-Term Pavement Performance Program, Publication No. FHWA-RD 03-031, June 2003.
Molenaar, A.A.A., Bottom-Up Fatigue Cracking: Myth or Reality? in Proc of 5th International RILEM Conference, Limoges, France, 2004. pp. 275-282.
Molenaar, A.A.A., Structural Performance and Design of Flexible Road Construction and asphalt Concrete Overlays, Ph.D Thesis, Delft University of Technology, the Netherlands, 1983.
Pell, P. S., Fatigue Characteristics of Bitumen and Bituminous Mixes, Proceedings, International Conference on the Structural Design of Asphalt Pavements, 1962.
9
Pronk, A.C., The theory of the four point dynamic bending test-Part 1. Report P-DWW-96-008, Rijkswaterstaat, the Netherlands, 1996.
Roberts FL, Kandhal PS, Brown ER, Lee DY, Kennedy TW, Hot Mix Asphalt Materials, Mixture Design, and Construction. NAPA Education Foundation, Second Edition. 1996, pp. 603.
Strategic Highway Research Program (SHRP), Fatigue response of asphalt-aggregate mixes, Executive summary, National Research Council, 1992.
Tangella, S. R., Craus, J., Deacon, J. A. and Monismith, C. L., Summary report on fatigue response of asphalt mixtures, SHRP Report No. TM-UCB-A-003-A, 1990.
Uhlmeyer, Jeff S., Willoughby, Kim. Top-down Cracking in Washington State Asphalt Concrete Wearing Courses.". Journal of the Transportation Research Board, 2000, Vol. 1730, pp.110-116.
Uhlmeyer, J.S.; Willoughby, K.; Pierce, L.M. and Mahoney, J.P., Top-Down Cracking in Washington State Asphalt Concrete Wearing Courses. Transportation Research Record 1730. Transportation Research Board, National Research Council, Washington, D.C. 2000. pp. 110-116.
van Dijk, W., Practical fatigue characterization of bituminous mixes, Proceedings of the Association of Asphalt Paving Technologists, 1975, pp. 38.
11
Chapter 2 Literature Review
The literature survey on fatigue testing of asphalt mixtures in the laboratory is presented in this chapter. Since in this project, the test type and specimen size effect on the laboratory fatigue results are involved, this Chapter is mainly focused on the following issues.
Section 2.1 provides the background regarding the fatigue research on asphalt mixture. In Section 2.2, the widely used laboratory fatigue tests for measuring fatigue behavior of asphalt mixtures are discussed. Some factors affecting fatigue results are summarized in Section 2.3. In Section 2.4, the different analysis approaches to characterize fatigue are reviewed, including the classical analysis, the dissipated energy approach and the fracture mechanics approach. Section 5 discusses some fatigue models which are used to describe the influence of test type and specimen size on the fatigue behavior of asphalt mixtures.
2.1 Background of Fatigue Research on Asphalt Mixtures
The first fatigue study was initially done on metal. Richard [1988] stated that Wöhler [1860] conducted systematic investigations of fatigue failure in railroad axles for the German railway industry. His work also led to the characterization of fatigue behavior in terms of stress amplitude-life (S-N) curves.
Fatigue considerations in the design of bituminous pavements date back to the early 1940s due to a significant increase in the traffic volume and the magnitude of wheel loads. Many flexible pavement researchers and designers expressed their concern over the fatigue failure of pavements under various loading conditions. Porter noted that flexible pavements failed under deflections as small as 0.02 to 0.03 inch (0.5-0.8 mm) [Porter, 1942]. In 1953, Nijboer and van der Poel showed that cracks which often appeared in the later stages of the life of an asphaltic concrete could be related to the bending stress induced by the moving traffic, exceeding the flexural strength of the material [Nijboer, 1953]. Examinations of the results of the AASHTO Road Test also revealed that cracking and initial failure of the pavement were primarily caused by repeated bending of the bituminous layers. Hveem F.N. [1955] reported fatigue failure caused by repeated loading on asphalt pavements built on highly resilient soils. Hveem concluded that there was a correlation between observations of cracking, fatigue type failures in bituminous pavements, and the measured repeated deflections that the pavement undergoes with each passing wheel.
However, it is not fully clear which chemical, physical, and mechanical processes exactly occur in fatigue. It is generally known that, during the fatigue process, successive stages of deterioration occur. These are often named: initiation of microcracks, propagation of microcracks, initiation/formation of macrocracks or coalescence of microcracks into macrocracks, propagation of macrocracks, disintegration or rupture/failure. The use of fundamental, non-empirical mechanical tests to characterize the fatigue behavior of these
12
materials is particularly important when designing and predicting the in-service performance of asphalt mixtures.
2.2 Laboratory Fatigue Test Methods
Over the past 60 years, a number of test methods have been developed to simulate the fatigue behavior of bituminous road construction materials. According to the mode of loading the most commonly used tests are classified in three groups, simple flexure, direct uniaxial loading and diametral loading tests, as mentioned in Section 1.3 [Tangella, 1990]. According to the stress-strain distribution in the specimen, the fatigue tests are divided into two types, the homogenous type and inhomogeneous type. If the stress-strain distribution is uniform throughout the specimen, the test is called homogeneous test. An example is the uniaxial loading test. For non-homogeneous tests, such as bending tests and the indirect tensile test, the stress-strain field is not uniform along the specimen and cross section.
2.2.1 Simple Flexure Test
2.2.1.1 Two-Point Bending (2PB) Test
Two-point bending tests on trapezoidal specimens were conducted by researchers of Shell [van Dijk, 1975], the Center of Road Research in Belgium [Verstraeten, 1972], and LCPC researchers [Bonnot, 1986]. Figure 2-1 illustrates the LCPC equipment. The smaller end is subjected to either a sinusoidal displacement [Bonnot, 1986] [van Dijk, 1975] [Verstraeten, 1972] or load [Kunst, 1989]. By properly selecting the dimensions of the trapezoid, the specimen will fail at about mid height where the bending stress is largest and not at the base where the bending moment is largest and the boundary conditions might adversely affect interpretation of test the results. Specimens tested by van Dijk had a base cross section of 55 mm by 20 mm, a top cross section of 20 mm by 20 mm, and a height of 250 mm.
Figure 2-1 2PB fatigue test machine with a trapezoidal specimen [Chkir, 2009] According to EN 12697-24 [EN, 2003], the specimens shall be of an isosceles trapezoidal shape as shown in Figure 2-2, for which the dimensions are given in Table 2-1. The large
Specimen
Displacement sensor
13
base of each specimen should be glued in a groove (about 2mm deep) of a metal base having a minimum thickness of 20mm, as shown in Figure 2-1. The specimen shall be moved sinusoidally at its head at the imposed displacement amplitude until the failure criterion has been reached. The deformation shall be such that at least one third of the element tests provide results with N ≤ 106 and at least one third of the element tests provide results with N ≥ 106.
Table 2-1 Dimensions of the 2PB specimen Type of mixture D ≤ 14mm 14 < D ≤ 20mm 20 < D ≤ 40mm B 56 70 70 b 25 25 25 e 25 25 50 h 250 250 250
D: maximum aggregate size of asphalt mixture
2.2.1.2 Three-Point Bending Test
At the Shell Laboratory in Amsterdam, van Dijk [1972] used the center-point loading equipment. The specimen dimensions are 30 mm (1.2 in.) × 40 mm (1.6 in.)× 230 mm (9.2 in.), tests were done in the controlled-deflection (strain) mode. Figure 2-3 shows the test apparatus and the scheme of three point bending test.
(a)
(b)
Figure 2-3 Three point bending test apparatus scheme (a) and load characteristics (b) B
h e
e b
Figure 2-2 Geometry of the specimens
F0
14
According to EN 12697-24 [EN, 2003], the dimensions of the test beams shall be (300 ± 10) mm × (50 ± 3) mm × (50 ± 3) mm. The specimen shall be clamped to the support mechanism through the two metallic tubes glued to one of its faces and to the piston rod through the tube glued to the opposite face. The support mechanism shall be capable of moving and tilting its axes. Specimens and extensometer are assembled and brought to the test temperature, 20 ºC. A cyclic sinusoidal displacement of the piston rod shall be applied. The wave frequency shall be 10Hz, and the values of the total amplitude usually range from 80 µm to 350 µm depending on the mixture.
2.2.1.3 Four-Point Bending Test
According to Molenaar [Molenaar, 1987], the specimens for the four-point bending test, can be obtained in the following way. Slabs of about 0.6 × 0.6 m2 are sawn from the AC pavement. From the bottom layer of these slabs, beams are sawn with dimensions of 450 mm × 50 mm × 50 mm, with the length perpendicular to the direction of traffic. For the four-point bending tests, a servo-hydraulic testing rig is used. The setup is schematically shown in Figure 2-4. The distance between the outer supports is 400 mm, between the inner supports 130 mm. The tests are executed with a displacement-controlled fully sinusoidal load signal at 30 Hz and the range of the test temperature is 0~20 ºC. Generally, different preset displacements are chosen, which will result in an expected fatigue life of 105 to 106 load repetitions.
Figure 2-4 Schematic diagram of the four-point bending test
According to the ASTM standard D 7460 [ASTM, 1996], the dimensions of the test beam are 380 (length) × 50 (height) × 63 (width) mm. The horizontal spacing of the clamps is 119mm. Before testing, the specimen is placed in an environment which is at 20 ± 0.5 ºC for two hours. The desired initial strain (250 to 750 microstrain) and loading frequency (5 to 10Hz) are selected. The initial stiffness of the specimen is determined at the 50th load cycle, which is used as a reference for determining specimen failure. A deflection level (strain level) is selected such that the specimen will undergo a minimum of 10000 load cycles before its stiffness is reduced to 50 percent or less of the initial stiffness.
15
Figure 2-5 Scheme of the four-point bending test and load characteristics [ASTM, 1996]
2.2.1.4 Rotating Bending Test
(a) Controlled-Stress Rotating Flexure (b) Failure specimen
Figure 2-6 Flexure apparatus used by Pell [Pell, 1965] and specimen before and after testing [Saal, 1960]
At the University of Nottingham, U. K. [Pell et al., 1975 and 1973a] a rotating cantilever machine (Figure 2-6a) was used in which the specimen is mounted vertically on a
bearing Loading head specimen seat housing bearings & electric motor
rev. counter stop switch weights tank wire pulleys shaft chuck
16
rotating cantilever shaft and a single point load is applied through a bearing at the top. This loading system results in a sinusoidally varying bending stress of constant amplitude at any particular cross section of the specimen. Under this system of loading there is no shear stress on the specimen. The specimens were tested in a controlled temperature bath. The majority of the tests were carried out at a temperature of 10°C and a speed of 1,000 rpm. Specimens of the shape have a minimum diameter at the neck of 2.5 in. Figure 2-6b shows a demoulded specimen ready for testing and also a broken specimen which has failed in fatigue after testing.
2.2.2 Direct Axial Loading Test
Raithby [Raithby, 1972a] developed this form of fatigue testing at the Transport and Road Research Laboratory (TRRL) in the United Kingdom. Axial tensile and compressive loading was applied using a servo-controlled electro-hydraulic machine. Specimens were prismoidal, with a 75 mm2 cross section and a length of 225 mm (Figure 2-7). Aluminum caps are glued upon the ends of the specimens, in such a way that these can be mounted in a servo-controlled hydraulic MTS testing machine. Loading frequencies were 16.7 and 25 Hz, and the effects of rest periods, shape of wave form, and the sequence of load application (compression/tension, tension/compression, compression only, and tension only) were evaluated.
Figure 2-7 Schematic representation of a direct axial fatigue test [Raithby, 1972a] Molenaar [1983] selected the direct tensile test for crack growth experiments. The sketch and picture of the test set-up as used are given in Figure 2-8.
Temperature chamber LVDT Command signal Hydraulic Power supply Error signal amplifier Summing junction C.R.O. Hydraulic actuator Servo-valve Load cell
17
Figure 2-8 Set-up of direct tensile test [Molenaar, 1983]
The specimens used in the test were about 0.15 m long and the cross section was approximately 0.05 × 0.05 m. At mid length, an artificial crack was sawn at two opposite sides which had a depth of about 0.005 m. The beam specimens were sawn from slabs. An epoxy resin was used to glue the specimens to the top and bottom loading plate. To ensure a proper alignment of the specimens, hardening of the glue took place while the beam was positioned under the ram of the dynamic loading system. The shape of the load pulse was a haversine and a load to rest period ratio of 1 to 7 was used. During the tests the elastic vertical displacement was continuously recorded.
2.2.3 Diametral Loading Test (Indirect Tensile Test)
Indirect tension testing is done by applying a compressive force to a cylindrical specimen along its vertical diameter to produce tensile stresses perpendicular to the loading axis. Figure 2-9 shows a schematic of the indirect tensile test.
Figure 2-9 Schematic of indirect tension test
Pressure cell steel plate epoxy resin specimen epoxy resin steel plate LVDT Range ± 1 mm holder Loading strip Specimen Compressive force
18
The test was developed and has been used since the early 1970s to characterize bituminous materials in terms of strength and elastic stiffness [Kennedy, 1968] [Schmidt, 1971]. Since that time the repeated load indirect tensile fatigue test is widely used to evaluate the fatigue properties of asphalt materials by a number of investigators [Kennedy, 1983] [Khosla and Omer, 1985] [Tangella, 1990]. In the UK this test has also been developed as a simple fatigue tool conducted as one of the test modules in the Nottingham Asphalt Tester (NAT) [Brown, 1995].
Normally a haversine load pulse is employed in the test and the diametral specimen is assumed to fail near the load line. Three types of failure patterns were usually observed [Sousa, 1991]: (1) crack initiation at or near the center of the specimen, resulting in complete splitting of the specimen; (2) crack initiation at the top of the specimen, progressively spreading downward in a V-shape, the arms of which originate from the outside edges of the loading platen; and (3) no real cracking occurs, with the specimen being plastically deformed beyond the limiting vertical deformation.
Due to the absence of stress reversal, the accumulation of permanent deformation increases. The possibility that under high loads and/or high temperatures either compressive or shear failure occurs in the specimen. Fatigue fracture under indirect tensile loading ideally should occur by splitting of the specimen in two halves with minimum permanent deformation. Read and Collop recommended that the loading time should be 120 ms and test temperatures should be less than 30°C [Read, 1997].
2.3 Influence of Test Type, Specimen Size and Test Conditions
on Fatigue Results
The European Committee for Standardization (CEN) specifies several tests for characterizing the fatigue of bituminous mixtures, as follows:
1) Two-point bending test on trapezoidal shaped specimens 2) Two-point bending test on prismatic shaped specimens 3) Three-point bending test on prismatic shaped specimens 4) Four-point bending test on prismatic shaped specimens 5) Indirect tensile test on cylindrical shaped specimens
Figure 2-10 shows a schematic illustrating all of the allowed fatigue test methods. Most of these test methods are already discussed in Section 2.2. Because the European Standard does not impose a particular type of testing device, the choice of the test methods and the test conditions depends on the possibilities and the working range of the used device. This might lead to incomparable results obtained from the different test methods. Therefore it is necessary to investigate the influence of the test type, specimen size and some important test conditions on the fatigue results.
19
Figure 2-10 Schematics of the laboratory fatigue tests recommended by the European Committee for Standardization [EN 12697-24, 2003]
2.3.1 Influence of Test Type and Specimen Size
2.3.1.1 Influence of Test Type
A certain bituminous material may show different fatigue results dependent on the various geometries (beam, trapezoidal, cantilever beam, cylinder and other special shapes) and the different types of loading (bending, tension-compression and shear). Many researchers compared the results from different types of fatigue tests. Aguirre et al, found that fatigue lives are shorter in tension-compression than in bending at the same nominal strain, as shown in Figure 2-11 [Aguirre, 1981].
0.00001 0.0001 0.001 1000 10000 100000 1000000 10000000 N cycles In it ia l s tr a in Flexion (labo1) Flexion (labo2) Traction Compression (labo3) Traction Compression (labo4) Traction Compression (labo5)
Figure 2-11 Fatigue behavior at constant stress amplitude (10°C, 10Hz) [Aguirre, 1981]
(1) (2) (3)
20
Di Benedetto H. et al, reported results from an inter-laboratory investigation organized by the RILEM 182-PEB Technical Committee [Di Benedetto, 2004]. Eleven (11) different test types, including uniaxial tension/compression, 2-, 3- and 4-point bending and indirect-tension tests, were used to evaluate fatigue characteristics of a dense grade asphalt concrete mixture. The loading signal was specified as sinusoidal at a frequency of 10 Hz and a test temperature of 10 °C was chosen.
Figure 2-12 shows fatigue results of the used 11 test types. The obtained fatigue lives are significantly influenced by the test method used. The Indirect Tension Test (ITT) shows the shortest fatigue life due to accumulation of permanent deformation in addition to the fatigue damage. For a given strain amplitude, the beam tests generally result in longer life durations compared to T/C (Tension/Compression) tests. The strain value, ε6, which
represents the failure at one million cycles, is plotted in Figure 2-13. The ITT has the smallest strain value, ε6, but this value can not be compared with the other
strain-controlled tests.
Figure 2-12 Fatigue lives for strain controlled fatigue tests (except ITT)
Figure 2-13 Strain amplitude “ε6” giving failure at 106 cycles from different fatigue tests
80 1,E+09 1,E+08 1,E+07 1,E+06 1,E+05 1,E+04 1,E+03 100 110 ε0 (µm/m) Nf50 3PB 4PB 2PB T/C ITT Nf50 = α*ε^(-β) 30 50 70 90 110 130 150 170 190 T/C 2PB 4PB Average all ITT
21
According to de la Roche et al., the fatigue life is longer in three-point bending than in two-point bending [de la Roche, 1993]. The relationship of ε6 between these two tests is:
6(3 ) 6( 2 )
1.4
2
PB PBε
ε
=
∼
(2-1)2.3.1.2 Influence of Specimen Size
Doan carried out two-point bending tests to study the influence of the size effect on fatigue evaluation of trapezoidal specimens with different sizes [Doan, 1973]. He found that the specimen size effect was negligible leading to the same average fatigue life for similar specimen series.
Didier Bodin from LCPC, however, showed a significant effect of the trapezoidal beam size in bending fatigue tests [Bodin, 2006]. The fatigue line plots and ε6 of different sizes
are presented in Figure 2-14 (a) and (b). Size 1.0 corresponds to the standardized size. Size 0.5, the smaller beam, has a longer fatigue life compared to size 1.0 and size 2.0, the bigger beam. The value of ε6 is also a function of specimen size and decreases with
increasing size. 1000 10000 100000 1000000 10000000 100 140 180 220 260 Strain anplitude (10-6) F a ti g u e l if e NF ( 5 0 % ) size0.5 size1.0 size2.0 100 120 140 160 180 200 0 0.5 1 1.5 2 2.5 Size D/Do ε6 [ 1 0 -6] (a) (b)
Figure 2-14 Fatigue line fitted for each sample size (a) and values of ε6 versus the size of
the specimen sets in two-point bending test [Bodin, 2006]
Figure 2-15 shows the influence of the width b of a specimen on the fatigue life, Nf
[Jacobs, 1995]. At a chosen strain amplitude of 400 µm/m the ratio in fatigue life between a 50 and a 20 mm wide specimen is around 3.3; for a 250 mm wide specimen the ratio Nf(b=250)/Nf(b=20) is about 19.
22
Figure 2-15 Influence of the specimen width b on the fatigue life Nf [Jacobs, 1995]
For the four-point bending tests on beams with a notch subjected to half sine load, Groenendijk developed the function of the number of load repetitions to failure based on the Paris’ law [Groenendijk, 1998]:
( )
0( )
1 / 2 0.5 1.5 2.5 3.5 4.5 / / 1.99 2.47 12.97 23.17 24.8 f n c h n n n c h mix h d c h N A S c c c c c h h h h h ε − − = ⋅ − + − + ∫
(2-2)Where: c0 : initial crack length, [mm];
cf : maximum crack length for which stable crack occurs, [mm];
A,n : parameters depending on the material and on the experimental conditions;
c : crack length, [mm];
Smix : stiffness of asphalt mixture, [MPa];
ε : applied strain, [m/m];
h : height of the specimen, [mm].
2.3.2 Influence of Loading Mode
Normally one of two main modes of loading are applied in a fatigue test:
The load (stress) controlled mode – the amplitude of the applied load is held constant during the test.
b=250mm b=150mm b= 50 mm b= 20 mm
23
The displacement (strain) controlled mode – the amplitude of the applied deformation is held constant.
Strictly speaking it is the load or displacement which is controlled and the stress and strain are calculated from them. However, controlled stress and strain are commonly used terms.
Brown indicated that in the controlled stress mode, a repeated stress or load of constant amplitude is applied to a specimen which causes a gradual increase in strain at midspan and a gradual decrease of the stiffness [Brown, 1978]. The increase of strain is rather rapid at the end of the test, till complete fracture occurs. In controlled strain tests, the loading is applied such that the repeated deflection or strain stays constant during the test (see Figure 2-16). During the test the load will gradually decrease because of damage development. Most of the time no real failure will occur and it is therefore assumed that the specimen has failed if the load level has decreased to 50% of the original load level.
(a) (b)
Figure 2-16 Graphical representation of controlled stress (a) and controlled strain (b) modes of loading [Epps and Monismith, 1971]
Tayebali, et al [Tayebali, 1994] showed a typical plot (Figure 2-17) of the stiffness ratio (defined as quotient of stiffness at the ith load repetition to the initial stiffness, Si/S0)
versus the number of load repetitions for flexural beam fatigue tests in both controlled-stress and controlled-strain modes of loading. Obviously the stiffness ratio in the controlled-stress mode decreases more rapidly compared to the stiffness ratio results in controlled-strain mode.
