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Development of a double-torsion fracture test to predict channelized crack behaviors of asphalt concrete
Construction and Building Materials 26 (2012) 694–700
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of a double-torsion fracture test to predict channelized crack behaviors of asphalt concrete Hyunwook Kim ⇑, Manfred N. Partl Empa, Swiss Federal Laboratories for Materials Testing and Research, CH-8600 Dübendorf, Switzerland
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 20 June 2011 Accepted 23 June 2011 Available online 19 July 2011 Keywords: Bituminous materials Fracture Double-torsion Compliance Stress intensity factor
a b s t r a c t Fracturing of asphalt concrete paving surfaces and overlays is a significant cause of premature pavement deterioration. Fracture mechanics and the proper handling of crack propagation are much needed to understand the mechanisms that are relevant for increasing pavement life. The topic is still quite wide in the field of asphalt pavement design and analysis. This paper shows the experimental development of a double-torsion fracture test for predicting fundamental fracture properties of bituminous materials. Double-torsion test specimens were prepared from a model asphalt material using an automatic French slab compactor. Double-torsion tests were performed at low temperatures to investigate brittle and/or quasi-brittle behavior of bituminous materials. A constant displacement control method was applied to obtain reliable fracture properties of bituminous materials. Test geometry with different notch lengths was considered to obtain a standard specimen configuration without any unexpected failure. Characteristic fracture properties from double-torsion tests were determined based on the linear elastic fracture mechanics theory including compliance. Experimental results showed that the notch length was not a significant factor in the determination of stress intensity factor properties from double-torsion fracture tests on the model material used in this study. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Asphalt concrete is a quasi-brittle composite material, which is composed of brittle aggregates and viscous bituminous binder. Asphalt concrete becomes more brittle at low temperatures, especially under high frequency loading conditions, as shown in previous studies on the fracture behavior of asphalt concrete at low temperatures. Different test methods were used. Three-point bending beam tests were the popular application for investigating the fracture mechanism of asphalt concrete [1,2]. Also, disk-shaped compact tension tests and semi-circular tests were applied to study the fracture toughness of asphaltic materials [3–5]. However, a new fracture test method for considering the longitudinal crack behavior caused by traffic wheel loads was needed. In reality, there are many repeated traffic wheel loads on the pavement and they will make fatigue cracks through the direction of traffic loading. Authors wanted to develop a realistic fracture test to consider the channelized cracking by repeated traffic wheel loads as shown from the conceptual insight in Fig. 1. For a wide range of materials including ceramics [6–8], glasses [9], composites [10], cement concrete [11], polymers [12,13], steels ⇑ Corresponding author. Tel.: +41 44 823 4474; fax: +41 44 821 6244. E-mail addresses: [email protected], [email protected] (H. Kim). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.06.076
[14], and rocks [15,16], the double-torsion (DT) approach has been used in the fracture mechanics field for investigating both critical crack growth (fracture toughness measurement) and subcritical crack propagation. However, surprisingly, this method has not been applied for bituminous materials so far. Crack can start from a critical defect, growing very slowly at first, and then accelerating under further load until the part finally fails. This behavior is known as subcritical crack propagation. The advantages of DT tests are following: (1) the test configuration consists of simple specimen geometry and inexpensive experimental set-up; (2) the obtaining fracture property, the stress intensity factor, is the first approximation and independent of crack length for a range of crack lengths in DT specimens; (3) comprehensive crack measurements may not be needed when the constant loading techniques; and (4) DT tests can characterize both the crack channeling, which is a typical pavement longitudinal crack behavior, and fatigue cracking under repeated traffic loads. In this study, a DT fracture test for bituminous materials was developed and implemented to predict the crack channelizing and to obtain the fracture properties. In the beginning of study, there were many trial test configurations and specimen geometries for obtaining the reliable test results at low temperatures. DT tests were performed with different notch lengths and loading speeds to investigate the response dependencies of fracture behavior.
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H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700 Table 1 Marshall properties of AC4. Asphalt mixture (AC4) Percentage of binder Density Area density (SSD) Percentage of air void Voids in the mineral aggregate (VMA) Voids filled with asphalt (VFA)
8.0 2407 2296 4.6 22.5 79.4
Mass% kg/m3 kg/m3 vol.% vol.% vol.%
Marshall properties Marshall stability Marshall flow
11.1 2.7
kN mm
Fig. 1. Fatigue crack behavior caused by repeated traffic loads.
In addition, Trantina [25] used a finite element analysis to show that KI (the stress intensity factor in mode-I, pure tensile mode) was independent in an operational range with 5% deviations of KI. The operational range was
0:55w < a < l 0:65w
ð2Þ
According to the above constraint, the experimental study of Shetty and Virkar [26] determined as operational the following ranges of crack lengths:
Fig. 2. Aggregate gradation of asphalt mixture.
2. Materials Asphalt binder, bitumen 70/100, based on the penetration grade system according to the European standard EN 12591 [17] and commonly used for asphalt pavement surface mixtures in Switzerland was selected for this study. According to European Standard EN 13108-1 [18], asphalt mixture, AC4, with relatively small nominal maximum aggregate size was used as a model material to obtain homogeneous and repeatable test results. The aggregate gradation curve of asphalt mixture is shown in Fig. 2. Table 1 shows material properties of the asphalt mixture and Marshall test results following the series of European standards EN 12697-34 [19] and EN 12697-35 [20].
3. Experimental procedure 3.1. Specimen preparation Asphalt concrete slabs were compacted by an automatic steel roller compactor, developed by Laboratoire Central des Ponts et Chaussées (LCPC) in France [21]. The asphalt slabs were 500 mm long with a rectangular cross section of 180 width and 20 mm thickness. The constant load magnitude of the steel roller was 5 kN. The bottom plate of steel mold is gradually lifted during compaction such that the contact surface of the steel roller with the specimen always remains at a constant level during the roller passing. For compacting asphalt specimens, the hot asphalt concrete mixture was firstly filled into a pre-heated steel mold with an aluminum bottom plate and compacted until obtaining the targeted 20 mm specimen thickness. There have been some studies for finding proper DT specimen geometries with other materials. Evans and Wiederhorn [22] and Atkinson [23] showed experimentally that specimen width w should be 12 times greater than thickness d. Pletka et al. [24] suggested that the specimen length l should be greater than twice the value of w. Therefore, the size of the DT specimen should be
12d < w < l=2
ð1Þ
0:50w < a < l 1:0w
ð3Þ
0:4w < a < l 0:8w
ð4Þ
Most recently, Ciccotti et al. [27] performed detailed threedimensional finite element analyses for various range of DT test specimens (170 mm < l < 250 mm and 60 mm < w < 100 mm). They analyzed both the range determined by Trantina [25] and the dimension proposed by Shetty and Virkar [26]. Based on their investigations, the operational ranges were not consistent due to different loading conditions and different thickness. Also, they concluded that appreciable deviations can be from the classical analytical predictions of strain energy release rate (g). A guide groove is necessary to control the crack path in DT specimens due to the heterogeneity of materials. There were some studies related to the notch shape effects in DT fracture tests [15,28]. Swanson [29] mentioned that the guide groove geometries (sizes and shapes) had no significant effects of reducing the scatter of DT test on rocks. However, Nara and Kaneko [16] later tested rock DT specimens with three different groove shapes using rectangular, semi-circular, and the triangular section grooves. They concluded that the level of reproducibility was highest for the rectangular guide groove specimens. In this paper, the selected proper specimen dimension relied on previous DT studies but the specimen dimension was not limited to the definition from the previous studies because of different material characteristics, e.g. different level of heterogeneity like the relatively large aggregates embedded in asphalt mixtures and the viscous behavior from bituminous binder. Fig. 3 shows the specimen geometry for DT fracture tests. DT specimens were cut from asphalt slabs compacted by French roller compactor with dimensions as shown in Table 2. The thickness of 20 mm was chosen because the double-torsion fracture test concept was based on the thin plat theory and DT specimens should have enough thickness, more than three times than the maximum aggregate size, to reduce the aggregate dependency on test results. Beam length of 300 mm, twice than the width and more than six times than the thickness, was chosen to produce reasonable bending conditions within the size limitation of the temperature chamber. In this study, the rectangular guide groove was made on the bottom surface of DT specimen and the notch lengths (a) were varied with 0, 30, 60, and 85 mm.
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H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
A
A
wpx
differential transducer (LVDT) placed on the top surface in the middle of steel loading plate as shown in Fig. 4 (left). Fig. 4 (right) shows the details of DT loading point area and small pieces of rectangular steel plates on the bottom of loading points for avoiding punching effects at the loading positions. The test was conducted in a refrigerated environmental chamber capable of maintaining air temperature within ±0.2 °C during the test. The groove surface was located at the bottom surface of DT specimens because the critical cracking usually starts from the crack tip of bottom surface.
d
Groove
wpy
a
l
Notch 3.3. Determination of fracture parameters
wm
The DT fracture tests have received considerable attention as a direct method to determine the fracture toughness and the behavior of subcritical crack growth due to its simplicity and the possibility of conducting extensive crack propagation in a wide range of crack propagation rates under constant loading conditions or load relaxation tests [30]. A compliance analysis of DT fracture test indicates that the stress intensity factor, KI, is independent of the crack length a [12]. The compliance C of solid materials, defined as the ratio of load point displacement (D) to the load (P), varies linearly with crack length:
wo w
A
A
dl
Groove
gd gw
Fig. 3. Double-torsion specimen geometry.
C¼ Table 2 Dimension of double-torsion specimen (unit: mm). w
w0
wm
l
d
U
wpx
wpy
a
dl
gd
gw
150
10
65
300
20
10
20
20
0, 30, 60, 85
17
3
3
D ¼ Ba þ D P
where B and D are empirical constants depending on materials. The expression for stress intensity factor takes the following form:
K I ¼ Pwm 3.2. Testing method DT asphalt specimens were placed on simple supported bars inside of a temperature chamber under the mechanical loading frame and round-shape point loading pins with 10 mm diameters (U) applied on the top of DT specimens with 1 mm/min monotonic loading speed. The span length of supporting bars was 130 mm and the two loading bars were 40 mm apart. The distance between point loading positions and the outer edge of DT specimen was 20 mm. The diameter of supporting steel rollers was 10 mm. In most cases, two to four replicates were used for experiments. Mechanical loading was applied and monitored at 10 °C using a 10 kN load cell and the loading was controlled by the crosshead movement. The beam deflection was measured by A linear variable
ð5Þ
3ð1 þ mÞ
!1=2
3
wd dl wðd=wÞ
ð6Þ
where P is the applied force, m is Poisson’s ratio, dl is the ligament length after subtracting the groove depth from d, and w(d/w) is a correction factor for the specimen thickness [31] but thin specimens can be assumed as 1/3 [32]. The correction factor can be significant for beams thick relative to wide. The function of correction factor is
p 2d 2d þ 1:20 exp wðd=wÞ ¼ 1 0:6302 w w d
ð7Þ
The instantaneous crack length (ai) can be obtained then by the following equation:
ai ¼ a þ Dai ¼ a þ
Ci C0 B
Fig. 4. DT test configurations: test set-ups and measurement (left) and a double-torsion specimen under loading conditions (right).
ð8Þ
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
where a is the initial notch length, C0 was calculated for each test from the initial slope of P–D curve in its elastic portion, Ci was obtained from lines radiating from the origin as shown in Fig. 5. The theoretical crack propagation velocity (Vthe) can be calculated based on the following equation [22]:
V the ¼
dD=dt PB
ð9Þ
where dD/dt is the velocity of loading bar during the crack propagation test. The averaged experimental crack propagation velocity (Vexp) can be determined based on the stable crack propagation length and measured time as following:
V exp
Dac Dc D0 ¼ ¼ Dt Dt
ð10Þ
where Dac is the stable crack propagation length until reaching the catastrophic point (Dc) and Dt is the time spent for crack propagation. To determine the specific work of fracture, cwork, the work performed by the mechanical loading on the specimen can be calculated based on the entire stable crack propagation path [33]. From Fig. 6, the total energy was split into the critical energy (Uc) and the elastic energy (Uel). As shown in Eq. (11), the area under the force versus displacement curve up to the catastrophic propagation point was divided by the corresponding projected fracture surface area. The elastic energy stored in the system at the catastrophic propagation point was also subtracted from the work performed by the test machine. The work of fracture at catastrophic point is given by the following equation:
cwork ¼
Uc ¼ 2dl Dac
R Dc 0
ðP DÞdD 12 Pc Dc 2dl Dac
ð11Þ
where Pc and Dc are, respectively, the loading force and the vertical displacement at the point where catastrophic propagation begins, and Dac = aca0, with ac obtained from the compliance curve. Uc is presented in Fig. 6. 4. Results and discussion 4.1. Fracture behavior for DT specimens with different notch length The applied force versus displacement curves in DT tests represent the region of elastic deformation in the beginning of the curve and the region of stable crack propagation where the points begin to deviate from the straight line of elastic region including the plateau and the failure. Fig. 7 shows the applied force versus displacement curves for tested DT asphalt specimens with different notch lengths at 10 °C. In general, the length of stable cracking plateau becomes shorter as the notch length increases. It is understandable that specimens with longer ligaments can resist more against the applied force and have more displacement at the displacement measurement or loading position. Also, the change of initial slope in Fig. 7 showed that DT specimens with longer notches can have higher compliance or lower stiffness. However, the notch length did not significantly or systematically contribute the values of maximum force. Fig. 8 shows typical crack propagation through the guide grove made on the bottom surface of DT specimen and also the side view through the crack path of cracked specimens. The subcritical crack growth was not investigated in this paper because of using relatively thin specimens. From Fig. 8, the channelized crack in DT specimens well followed the guide groove path but was not a straight line. The crack propagation still showed the arbitrary crack path along the guide groove line to avoid the aggregates and/or to follow the weakest material points. In future, some crack detection or measurement approaches will be applied to determine the crack velocity and investigate the behavior of subcritical crack growth in thick DT specimens. The materials constants B and D were determined from the averaged compliance values and notch length as shown in Fig. 9. The determined equations for the compliance of test specimens extracted from the force versus displacement curves are:
C 0 ¼ 3:2 106 a þ 3:609 107
ð12Þ
C c ¼ 2:8 106 ac þ 7:660 107
ð13Þ
Fig. 5. Schematic of P–D curve and compliance.
Fig. 6. Graphic representation of the calculation of work of fracture.
697
Fig. 7. Applied force versus displacement curves for asphalt concrete.
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H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
Fig. 8. Cracked DT specimens: crack path through the guide groove (left) and cracked area surface along groove lines (right).
As already discussed, the critical stress intensity factor, KIC, can be determined from Eqs. (6) and (7). The assumed Poisson’s ratio was 0.35. Fig. 10 shows the critical stress intensity factor versus notch length plots with the average value of 1.351 MPa m1/2. The averaged deviation from KIC was 5% from the averaged KIC. As shown in Fig. 11, theoretical and experimental crack propagation velocities were determined by Eqs. (9) and (10) and measured experimental data. There was a good agreement between theoretical and experimental velocities. Averaged experimental crack propagation velocity can be determined based on the crack length (Dac), as shown in Fig. 12, determined by initial and critical compliances and measured time at each compliance value. The
averaged stable crack propagation length for DT specimens with different notch length was 112 mm. Fig. 12 shows that the notch length did not have any influence on the critical crack length. Figs. 13 and 14 show the distributions of applied energy, elastic energy, Uc, and work of fracture at different notch length. The averaged percentage of elastic energy from the applied energy to DT specimens was 64.3%. The averaged work of fracture was 235 J/m2.
Fig. 9. Averaged compliance versus notch length for asphalt concrete.
Fig. 11. Crack propagation velocity versus notch length.
Fig. 10. Mode-I stress intensity factor (KIC) versus notch length.
Fig. 12. Stable crack propagation length versus notch length.
4.2. Fracture behavior for DT specimens under different loading speeds Four different loading speeds, 0.5, 1, 2.5, and 5 mm/min, were applied to AC specimens at 10 °C with 30 mm notch length to
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
699
investigate the dependency of loading speed to the fracture behavior of DT specimens. From Fig. 15, different loading speed affects the whole fracture behavior of DT specimens including initial stiffness and the length of stable crack propagation. Fracture parameters obtained from DT specimens under different loading speeds can be found in Table 3. As shown in Fig. 16, the variation of work of fracture becomes larger with increasing loading speed. This means that the repeatability of DT fracture tests is better in the condition of slower loading speed. Also, the averaged stable crack propagation length becomes longer as the loading speed becomes slower (Fig. 17).
Fig. 13. Averaged energies obtained from DT specimens with different notch length.
Fig. 16. Work of fracture in DT asphalt specimens under different loading speeds.
Fig. 14. Work of fracture for DT asphalt specimens with different notch length.
Fig. 17. Stable crack propagation length under different loading speeds.
Fig. 15. P–d curves with different loading speeds.
Table 3 Calculated averaged fracture parameters under different loading speeds at 10 °C. Loading speed (mm/min)
Applied energy (N m)
Uel (N m)
0.5 1 2.5 5
2.52 2.38 2.16 2.32
1.64 1.64 1.59 1.93
Average
2.35
1.70
Uc (N m)
cwork (J/m2)
KIC (MPa m1/2)
0.88 0.74 0.57 0.39
245.57 265.69 224.70 233.84
1.377 1.460 1.598 1.545
0.65
242.45
1.491
Fig. 18. Experimental and theoretical crack propagation velocity under different loading speeds.
700
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
The favorable aspect of DT fracture is that DT tests should have long enough stable crack propagation length to obtain better repeatable test results. From Fig. 18 you see above, the theoretical crack propagation velocity becomes diverge from experimental crack propagation velocity as the loading speed becomes faster. Based on the data trends from Figs. 17 and 18, slower loading speeds will be better than fast loading speeds to predict the fracture behavior of asphalt materials using DT tests. 5. Summary and conclusions In this study, a double-torsion (DT) fracture test was developed and implemented to investigate the fracture behavior of asphalt concrete. DT test was initiated for understanding the channelized crack propagation and for obtaining various fracture parameters. One selected model asphalt mixture, AC4, was tested with different notch lengths to testify the developed DT fracture test set-ups and to find the proper DT specimen geometry and test configurations. Some conclusive remarks are: – Double-torsion fracture test was a suitable method to characterize the crack propagation along the longitudinal dimension of thin plate asphalt specimen. – The compliance approach with different notch lengths showed the strong benefits for obtaining characteristic material parameters from DT fracture tests without comprehensive measurements. The material constants for AC4 were 3.2 106 for B and 3.609 107 for D at 10 °C. – The constant fracture toughness KIC was obtained from DT specimens tested with different notched lengths. In other words, the fracture property obtained from DT tests was independent on the initial notch length of DT specimen. The averaged critical stress intensity factor of AC4 was 1.351 MPa m1/2. – DT specimens tested under slower loading speeds showed longer stable crack propagation length, which is favorable in DT fracture tests. More DT fracture tests at different temperatures should be conducted to characterize various asphalt materials and these are one of ongoing studies by authors. Also, there are further research topics related to DT fracture tests, which are fatigue fracture tests with DT specimens, advanced crack measurements using optical methods, and numerical modeling approaches for DT fracture tests to understand more detail fracture mechanisms. References [1] Wagoner MP, Buttlar WG, Paulino GH. Development of a single-edge notched beam test for asphalt concrete mixtures. J Test Eval 2005;33(6):452–60. [2] Kim H, Wagoner MP, Buttlar WG. Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test. Mater Struct 2009;42(5):677–89. [3] Xue L, Marasteanu M. Cohesive modeling of fracture in asphalt mixtures at low temperatures. Int J Fract 2005;136:285–308. [4] Kim H, Wagoner MP, Buttlar WG. Simulation of fracture behavior in asphalt concrete using a heterogeneous cohesive zone discrete element method. J Mater Civ Eng 2008;50(8):552–63.
[5] Kim H, Wagoner MP, Buttlar WG. Numerical fracture analysis on the specimen size dependency of asphalt concrete using a cohesive softening model. Constr Build Mater 2009;25(5):2112–20. [6] McHenry KD, Yonushonis T, Tressler RE. Low-temperature subcritical crack growth in silicon carbide and silicon nitride. J Am Ceram Soc 1976;59(5– 6):262–73. [7] Ebrahimi ME, Chevalier J, Fantozzi G. Slow crack-growth behavior of alumina ceramics. J Mater Res 2000;15(1):142–7. [8] Gremillard L, Chevalier J, Epicier T, Fantozzi G. Improving the durability of a biomedical-grade zirconia ceramic by the addition of silica. J Am Ceram Soc 2002;85(2):401–7. [9] Bhaduri SB. Direct measurement of subcritical crack growth rate in magnesium aluminosilicate glass by the indentation technique. Mater Lett 1991;12(5):373–5. [10] Frassine R. The application of double torsion testing to unidirectionally reinforced composite materials. J Compos Mater 1992;26(9):1339–50. [11] Hill R, Styles C. The influence of polymer chain length on the fracture toughness of polymer-modified portland cements. J Mater Sci Lett 1992;11(23):1555–8. [12] Williams DP, Evans AG. Method for studying slow crack growth. J Test Eval 1973;1(4):264–70. [13] Kulawansa DM, Langford SC, Dickinson JT. Scanning tunneling microscope observations of polymer fracture surfaces. J Mater Res 1992;7(5):1292–302. [14] Egan B J, Delatycki O. Evaluation of the crack shape and activation energy for fracture in double torsion fracture tests of high density polyethylene. J Mater Sci Lett 1995;14(5):340–3. [15] Ciccotti M, Negri N, Gonzato G, Mulargia F. Practical application of an improved methodology for the double torsion load relaxation method. Int J Rock Mech Min Sci 2001;38(4):569–76. [16] Nara Y, Kaneko K. Study of subcritical crack growth in andesite using the double torsion test. Int J Rock Mech Min Sci 2005;42:521–30. [17] European Standard EN 12591. Bitumen and bituminous binders specifications for paving grade bitumens. European Committee for Standardization (CEN), Brussels; 1999. [18] European Standard EN 13108-1:2006/AC. Bituminous mixtures – material specifications – Part 1: Asphalt concrete. European Committee for Standardization (CEN), Brussels; 2008. [19] European Standards EN 12697-34. Bituminous mixtures – test methods for hot mix asphalt – Part 35: Laboratory mixing. European Committee for Standardization (CEN), Brussels; 2004. [20] European Standards EN 12697-35. Bituminous mixtures – test methods for hot mix asphalt – Part 34: Marshall test. European Committee for Standardization (CEN), Brussels; 2004. [21] Laboratoire Central des Ponts et Chausse´es LCPC. Asphalt mixtures slabs compaction unit, Nantes, France; 1995. [22] Evans AG, Wiederhorn SM. Crack propagation and failure prediction in silicon nitride at elevated temperatures. J Mater Sci 1974;9(2):270–8. [23] Atkinson K. Subcritical crack growth in geological materials. J Geophys Res 1984;89:4077–114. [24] Pletka BJ, Fuller Jr ER, Koepke BG. An evaluation of double-torsion testing – experimental, vol. 678. ASTM STP; 1979. p. 19–37. [25] Trantina GG. Stress analysis of the double-torsion specimen. J Am Ceram Soc 1977;60:338–41. [26] Shetty DK, Virkar AV. Determination of the useful range of crack length in double torsion specimens. J Am Ceram Soc 1978;61(11):93–4. [27] Ciccotti M, Gonzato G, Mulargia F. The double torsion loading configuration for fracture propagation: an improved methodology for the load relaxation at constant displacement. Int J Rock Mech Min Sci 2000;37(7):1103–13. [28] Pabst RF, Weick J. Double-torsion measurements with and without a guiding notch. J Mater Sci 1981;16:836–8. [29] Swanson PL. Subcritical crack growth and other time- and environmentdependent behavior in crustal rocks. J. Geophys. Res. 1984;89:4137–52. [30] Outwater JO, Murphy MC, Kumble RG, Berry JT. Fracture toughness and slowstable cracking, vol. 559. ASTM STP; 1974. p.127–38. [31] Timoshenko S, Goodier JN. Theory of elasticity. 2nd ed. New York: McGraw Hill; 1951. [32] Evans AG. A method for evaluating the time-dependent failure characteristics of brittle materials and its applications to polycrystalline alumina. J Mater Sci 1972;7:1137–46. [33] Nakayama J. Direct measurement of fracture energies of brittle heterogeneous materials. J Am Ceram Soc 1965;48(11):583–7.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of a double-torsion fracture test to predict channelized crack behaviors of asphalt concrete Hyunwook Kim ⇑, Manfred N. Partl Empa, Swiss Federal Laboratories for Materials Testing and Research, CH-8600 Dübendorf, Switzerland
a r t i c l e
i n f o
Article history: Received 29 June 2010 Received in revised form 20 June 2011 Accepted 23 June 2011 Available online 19 July 2011 Keywords: Bituminous materials Fracture Double-torsion Compliance Stress intensity factor
a b s t r a c t Fracturing of asphalt concrete paving surfaces and overlays is a significant cause of premature pavement deterioration. Fracture mechanics and the proper handling of crack propagation are much needed to understand the mechanisms that are relevant for increasing pavement life. The topic is still quite wide in the field of asphalt pavement design and analysis. This paper shows the experimental development of a double-torsion fracture test for predicting fundamental fracture properties of bituminous materials. Double-torsion test specimens were prepared from a model asphalt material using an automatic French slab compactor. Double-torsion tests were performed at low temperatures to investigate brittle and/or quasi-brittle behavior of bituminous materials. A constant displacement control method was applied to obtain reliable fracture properties of bituminous materials. Test geometry with different notch lengths was considered to obtain a standard specimen configuration without any unexpected failure. Characteristic fracture properties from double-torsion tests were determined based on the linear elastic fracture mechanics theory including compliance. Experimental results showed that the notch length was not a significant factor in the determination of stress intensity factor properties from double-torsion fracture tests on the model material used in this study. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Asphalt concrete is a quasi-brittle composite material, which is composed of brittle aggregates and viscous bituminous binder. Asphalt concrete becomes more brittle at low temperatures, especially under high frequency loading conditions, as shown in previous studies on the fracture behavior of asphalt concrete at low temperatures. Different test methods were used. Three-point bending beam tests were the popular application for investigating the fracture mechanism of asphalt concrete [1,2]. Also, disk-shaped compact tension tests and semi-circular tests were applied to study the fracture toughness of asphaltic materials [3–5]. However, a new fracture test method for considering the longitudinal crack behavior caused by traffic wheel loads was needed. In reality, there are many repeated traffic wheel loads on the pavement and they will make fatigue cracks through the direction of traffic loading. Authors wanted to develop a realistic fracture test to consider the channelized cracking by repeated traffic wheel loads as shown from the conceptual insight in Fig. 1. For a wide range of materials including ceramics [6–8], glasses [9], composites [10], cement concrete [11], polymers [12,13], steels ⇑ Corresponding author. Tel.: +41 44 823 4474; fax: +41 44 821 6244. E-mail addresses: [email protected], [email protected] (H. Kim). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.06.076
[14], and rocks [15,16], the double-torsion (DT) approach has been used in the fracture mechanics field for investigating both critical crack growth (fracture toughness measurement) and subcritical crack propagation. However, surprisingly, this method has not been applied for bituminous materials so far. Crack can start from a critical defect, growing very slowly at first, and then accelerating under further load until the part finally fails. This behavior is known as subcritical crack propagation. The advantages of DT tests are following: (1) the test configuration consists of simple specimen geometry and inexpensive experimental set-up; (2) the obtaining fracture property, the stress intensity factor, is the first approximation and independent of crack length for a range of crack lengths in DT specimens; (3) comprehensive crack measurements may not be needed when the constant loading techniques; and (4) DT tests can characterize both the crack channeling, which is a typical pavement longitudinal crack behavior, and fatigue cracking under repeated traffic loads. In this study, a DT fracture test for bituminous materials was developed and implemented to predict the crack channelizing and to obtain the fracture properties. In the beginning of study, there were many trial test configurations and specimen geometries for obtaining the reliable test results at low temperatures. DT tests were performed with different notch lengths and loading speeds to investigate the response dependencies of fracture behavior.
695
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700 Table 1 Marshall properties of AC4. Asphalt mixture (AC4) Percentage of binder Density Area density (SSD) Percentage of air void Voids in the mineral aggregate (VMA) Voids filled with asphalt (VFA)
8.0 2407 2296 4.6 22.5 79.4
Mass% kg/m3 kg/m3 vol.% vol.% vol.%
Marshall properties Marshall stability Marshall flow
11.1 2.7
kN mm
Fig. 1. Fatigue crack behavior caused by repeated traffic loads.
In addition, Trantina [25] used a finite element analysis to show that KI (the stress intensity factor in mode-I, pure tensile mode) was independent in an operational range with 5% deviations of KI. The operational range was
0:55w < a < l 0:65w
ð2Þ
According to the above constraint, the experimental study of Shetty and Virkar [26] determined as operational the following ranges of crack lengths:
Fig. 2. Aggregate gradation of asphalt mixture.
2. Materials Asphalt binder, bitumen 70/100, based on the penetration grade system according to the European standard EN 12591 [17] and commonly used for asphalt pavement surface mixtures in Switzerland was selected for this study. According to European Standard EN 13108-1 [18], asphalt mixture, AC4, with relatively small nominal maximum aggregate size was used as a model material to obtain homogeneous and repeatable test results. The aggregate gradation curve of asphalt mixture is shown in Fig. 2. Table 1 shows material properties of the asphalt mixture and Marshall test results following the series of European standards EN 12697-34 [19] and EN 12697-35 [20].
3. Experimental procedure 3.1. Specimen preparation Asphalt concrete slabs were compacted by an automatic steel roller compactor, developed by Laboratoire Central des Ponts et Chaussées (LCPC) in France [21]. The asphalt slabs were 500 mm long with a rectangular cross section of 180 width and 20 mm thickness. The constant load magnitude of the steel roller was 5 kN. The bottom plate of steel mold is gradually lifted during compaction such that the contact surface of the steel roller with the specimen always remains at a constant level during the roller passing. For compacting asphalt specimens, the hot asphalt concrete mixture was firstly filled into a pre-heated steel mold with an aluminum bottom plate and compacted until obtaining the targeted 20 mm specimen thickness. There have been some studies for finding proper DT specimen geometries with other materials. Evans and Wiederhorn [22] and Atkinson [23] showed experimentally that specimen width w should be 12 times greater than thickness d. Pletka et al. [24] suggested that the specimen length l should be greater than twice the value of w. Therefore, the size of the DT specimen should be
12d < w < l=2
ð1Þ
0:50w < a < l 1:0w
ð3Þ
0:4w < a < l 0:8w
ð4Þ
Most recently, Ciccotti et al. [27] performed detailed threedimensional finite element analyses for various range of DT test specimens (170 mm < l < 250 mm and 60 mm < w < 100 mm). They analyzed both the range determined by Trantina [25] and the dimension proposed by Shetty and Virkar [26]. Based on their investigations, the operational ranges were not consistent due to different loading conditions and different thickness. Also, they concluded that appreciable deviations can be from the classical analytical predictions of strain energy release rate (g). A guide groove is necessary to control the crack path in DT specimens due to the heterogeneity of materials. There were some studies related to the notch shape effects in DT fracture tests [15,28]. Swanson [29] mentioned that the guide groove geometries (sizes and shapes) had no significant effects of reducing the scatter of DT test on rocks. However, Nara and Kaneko [16] later tested rock DT specimens with three different groove shapes using rectangular, semi-circular, and the triangular section grooves. They concluded that the level of reproducibility was highest for the rectangular guide groove specimens. In this paper, the selected proper specimen dimension relied on previous DT studies but the specimen dimension was not limited to the definition from the previous studies because of different material characteristics, e.g. different level of heterogeneity like the relatively large aggregates embedded in asphalt mixtures and the viscous behavior from bituminous binder. Fig. 3 shows the specimen geometry for DT fracture tests. DT specimens were cut from asphalt slabs compacted by French roller compactor with dimensions as shown in Table 2. The thickness of 20 mm was chosen because the double-torsion fracture test concept was based on the thin plat theory and DT specimens should have enough thickness, more than three times than the maximum aggregate size, to reduce the aggregate dependency on test results. Beam length of 300 mm, twice than the width and more than six times than the thickness, was chosen to produce reasonable bending conditions within the size limitation of the temperature chamber. In this study, the rectangular guide groove was made on the bottom surface of DT specimen and the notch lengths (a) were varied with 0, 30, 60, and 85 mm.
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A
A
wpx
differential transducer (LVDT) placed on the top surface in the middle of steel loading plate as shown in Fig. 4 (left). Fig. 4 (right) shows the details of DT loading point area and small pieces of rectangular steel plates on the bottom of loading points for avoiding punching effects at the loading positions. The test was conducted in a refrigerated environmental chamber capable of maintaining air temperature within ±0.2 °C during the test. The groove surface was located at the bottom surface of DT specimens because the critical cracking usually starts from the crack tip of bottom surface.
d
Groove
wpy
a
l
Notch 3.3. Determination of fracture parameters
wm
The DT fracture tests have received considerable attention as a direct method to determine the fracture toughness and the behavior of subcritical crack growth due to its simplicity and the possibility of conducting extensive crack propagation in a wide range of crack propagation rates under constant loading conditions or load relaxation tests [30]. A compliance analysis of DT fracture test indicates that the stress intensity factor, KI, is independent of the crack length a [12]. The compliance C of solid materials, defined as the ratio of load point displacement (D) to the load (P), varies linearly with crack length:
wo w
A
A
dl
Groove
gd gw
Fig. 3. Double-torsion specimen geometry.
C¼ Table 2 Dimension of double-torsion specimen (unit: mm). w
w0
wm
l
d
U
wpx
wpy
a
dl
gd
gw
150
10
65
300
20
10
20
20
0, 30, 60, 85
17
3
3
D ¼ Ba þ D P
where B and D are empirical constants depending on materials. The expression for stress intensity factor takes the following form:
K I ¼ Pwm 3.2. Testing method DT asphalt specimens were placed on simple supported bars inside of a temperature chamber under the mechanical loading frame and round-shape point loading pins with 10 mm diameters (U) applied on the top of DT specimens with 1 mm/min monotonic loading speed. The span length of supporting bars was 130 mm and the two loading bars were 40 mm apart. The distance between point loading positions and the outer edge of DT specimen was 20 mm. The diameter of supporting steel rollers was 10 mm. In most cases, two to four replicates were used for experiments. Mechanical loading was applied and monitored at 10 °C using a 10 kN load cell and the loading was controlled by the crosshead movement. The beam deflection was measured by A linear variable
ð5Þ
3ð1 þ mÞ
!1=2
3
wd dl wðd=wÞ
ð6Þ
where P is the applied force, m is Poisson’s ratio, dl is the ligament length after subtracting the groove depth from d, and w(d/w) is a correction factor for the specimen thickness [31] but thin specimens can be assumed as 1/3 [32]. The correction factor can be significant for beams thick relative to wide. The function of correction factor is
p 2d 2d þ 1:20 exp wðd=wÞ ¼ 1 0:6302 w w d
ð7Þ
The instantaneous crack length (ai) can be obtained then by the following equation:
ai ¼ a þ Dai ¼ a þ
Ci C0 B
Fig. 4. DT test configurations: test set-ups and measurement (left) and a double-torsion specimen under loading conditions (right).
ð8Þ
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
where a is the initial notch length, C0 was calculated for each test from the initial slope of P–D curve in its elastic portion, Ci was obtained from lines radiating from the origin as shown in Fig. 5. The theoretical crack propagation velocity (Vthe) can be calculated based on the following equation [22]:
V the ¼
dD=dt PB
ð9Þ
where dD/dt is the velocity of loading bar during the crack propagation test. The averaged experimental crack propagation velocity (Vexp) can be determined based on the stable crack propagation length and measured time as following:
V exp
Dac Dc D0 ¼ ¼ Dt Dt
ð10Þ
where Dac is the stable crack propagation length until reaching the catastrophic point (Dc) and Dt is the time spent for crack propagation. To determine the specific work of fracture, cwork, the work performed by the mechanical loading on the specimen can be calculated based on the entire stable crack propagation path [33]. From Fig. 6, the total energy was split into the critical energy (Uc) and the elastic energy (Uel). As shown in Eq. (11), the area under the force versus displacement curve up to the catastrophic propagation point was divided by the corresponding projected fracture surface area. The elastic energy stored in the system at the catastrophic propagation point was also subtracted from the work performed by the test machine. The work of fracture at catastrophic point is given by the following equation:
cwork ¼
Uc ¼ 2dl Dac
R Dc 0
ðP DÞdD 12 Pc Dc 2dl Dac
ð11Þ
where Pc and Dc are, respectively, the loading force and the vertical displacement at the point where catastrophic propagation begins, and Dac = aca0, with ac obtained from the compliance curve. Uc is presented in Fig. 6. 4. Results and discussion 4.1. Fracture behavior for DT specimens with different notch length The applied force versus displacement curves in DT tests represent the region of elastic deformation in the beginning of the curve and the region of stable crack propagation where the points begin to deviate from the straight line of elastic region including the plateau and the failure. Fig. 7 shows the applied force versus displacement curves for tested DT asphalt specimens with different notch lengths at 10 °C. In general, the length of stable cracking plateau becomes shorter as the notch length increases. It is understandable that specimens with longer ligaments can resist more against the applied force and have more displacement at the displacement measurement or loading position. Also, the change of initial slope in Fig. 7 showed that DT specimens with longer notches can have higher compliance or lower stiffness. However, the notch length did not significantly or systematically contribute the values of maximum force. Fig. 8 shows typical crack propagation through the guide grove made on the bottom surface of DT specimen and also the side view through the crack path of cracked specimens. The subcritical crack growth was not investigated in this paper because of using relatively thin specimens. From Fig. 8, the channelized crack in DT specimens well followed the guide groove path but was not a straight line. The crack propagation still showed the arbitrary crack path along the guide groove line to avoid the aggregates and/or to follow the weakest material points. In future, some crack detection or measurement approaches will be applied to determine the crack velocity and investigate the behavior of subcritical crack growth in thick DT specimens. The materials constants B and D were determined from the averaged compliance values and notch length as shown in Fig. 9. The determined equations for the compliance of test specimens extracted from the force versus displacement curves are:
C 0 ¼ 3:2 106 a þ 3:609 107
ð12Þ
C c ¼ 2:8 106 ac þ 7:660 107
ð13Þ
Fig. 5. Schematic of P–D curve and compliance.
Fig. 6. Graphic representation of the calculation of work of fracture.
697
Fig. 7. Applied force versus displacement curves for asphalt concrete.
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Fig. 8. Cracked DT specimens: crack path through the guide groove (left) and cracked area surface along groove lines (right).
As already discussed, the critical stress intensity factor, KIC, can be determined from Eqs. (6) and (7). The assumed Poisson’s ratio was 0.35. Fig. 10 shows the critical stress intensity factor versus notch length plots with the average value of 1.351 MPa m1/2. The averaged deviation from KIC was 5% from the averaged KIC. As shown in Fig. 11, theoretical and experimental crack propagation velocities were determined by Eqs. (9) and (10) and measured experimental data. There was a good agreement between theoretical and experimental velocities. Averaged experimental crack propagation velocity can be determined based on the crack length (Dac), as shown in Fig. 12, determined by initial and critical compliances and measured time at each compliance value. The
averaged stable crack propagation length for DT specimens with different notch length was 112 mm. Fig. 12 shows that the notch length did not have any influence on the critical crack length. Figs. 13 and 14 show the distributions of applied energy, elastic energy, Uc, and work of fracture at different notch length. The averaged percentage of elastic energy from the applied energy to DT specimens was 64.3%. The averaged work of fracture was 235 J/m2.
Fig. 9. Averaged compliance versus notch length for asphalt concrete.
Fig. 11. Crack propagation velocity versus notch length.
Fig. 10. Mode-I stress intensity factor (KIC) versus notch length.
Fig. 12. Stable crack propagation length versus notch length.
4.2. Fracture behavior for DT specimens under different loading speeds Four different loading speeds, 0.5, 1, 2.5, and 5 mm/min, were applied to AC specimens at 10 °C with 30 mm notch length to
H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700
699
investigate the dependency of loading speed to the fracture behavior of DT specimens. From Fig. 15, different loading speed affects the whole fracture behavior of DT specimens including initial stiffness and the length of stable crack propagation. Fracture parameters obtained from DT specimens under different loading speeds can be found in Table 3. As shown in Fig. 16, the variation of work of fracture becomes larger with increasing loading speed. This means that the repeatability of DT fracture tests is better in the condition of slower loading speed. Also, the averaged stable crack propagation length becomes longer as the loading speed becomes slower (Fig. 17).
Fig. 13. Averaged energies obtained from DT specimens with different notch length.
Fig. 16. Work of fracture in DT asphalt specimens under different loading speeds.
Fig. 14. Work of fracture for DT asphalt specimens with different notch length.
Fig. 17. Stable crack propagation length under different loading speeds.
Fig. 15. P–d curves with different loading speeds.
Table 3 Calculated averaged fracture parameters under different loading speeds at 10 °C. Loading speed (mm/min)
Applied energy (N m)
Uel (N m)
0.5 1 2.5 5
2.52 2.38 2.16 2.32
1.64 1.64 1.59 1.93
Average
2.35
1.70
Uc (N m)
cwork (J/m2)
KIC (MPa m1/2)
0.88 0.74 0.57 0.39
245.57 265.69 224.70 233.84
1.377 1.460 1.598 1.545
0.65
242.45
1.491
Fig. 18. Experimental and theoretical crack propagation velocity under different loading speeds.
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The favorable aspect of DT fracture is that DT tests should have long enough stable crack propagation length to obtain better repeatable test results. From Fig. 18 you see above, the theoretical crack propagation velocity becomes diverge from experimental crack propagation velocity as the loading speed becomes faster. Based on the data trends from Figs. 17 and 18, slower loading speeds will be better than fast loading speeds to predict the fracture behavior of asphalt materials using DT tests. 5. Summary and conclusions In this study, a double-torsion (DT) fracture test was developed and implemented to investigate the fracture behavior of asphalt concrete. DT test was initiated for understanding the channelized crack propagation and for obtaining various fracture parameters. One selected model asphalt mixture, AC4, was tested with different notch lengths to testify the developed DT fracture test set-ups and to find the proper DT specimen geometry and test configurations. Some conclusive remarks are: – Double-torsion fracture test was a suitable method to characterize the crack propagation along the longitudinal dimension of thin plate asphalt specimen. – The compliance approach with different notch lengths showed the strong benefits for obtaining characteristic material parameters from DT fracture tests without comprehensive measurements. The material constants for AC4 were 3.2 106 for B and 3.609 107 for D at 10 °C. – The constant fracture toughness KIC was obtained from DT specimens tested with different notched lengths. In other words, the fracture property obtained from DT tests was independent on the initial notch length of DT specimen. The averaged critical stress intensity factor of AC4 was 1.351 MPa m1/2. – DT specimens tested under slower loading speeds showed longer stable crack propagation length, which is favorable in DT fracture tests. More DT fracture tests at different temperatures should be conducted to characterize various asphalt materials and these are one of ongoing studies by authors. Also, there are further research topics related to DT fracture tests, which are fatigue fracture tests with DT specimens, advanced crack measurements using optical methods, and numerical modeling approaches for DT fracture tests to understand more detail fracture mechanisms. References [1] Wagoner MP, Buttlar WG, Paulino GH. Development of a single-edge notched beam test for asphalt concrete mixtures. J Test Eval 2005;33(6):452–60. [2] Kim H, Wagoner MP, Buttlar WG. Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test. Mater Struct 2009;42(5):677–89. [3] Xue L, Marasteanu M. Cohesive modeling of fracture in asphalt mixtures at low temperatures. Int J Fract 2005;136:285–308. [4] Kim H, Wagoner MP, Buttlar WG. Simulation of fracture behavior in asphalt concrete using a heterogeneous cohesive zone discrete element method. J Mater Civ Eng 2008;50(8):552–63.
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