Modelling crack initiation in bituminous binders under a rotational shear fatigue load

TL;DR: In this article, an energy-based crack initiation criterion is developed for bitumen under a rotational shear fatigue load, based on a damage mechanics analysis of fatigue cracking process, the crack initiation is defined and local energy redistribution around crack tips due to factory-roof cracking is quantified.

About: This article is published in International Journal of Fatigue.The article was published on 2020-10-01 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Damage mechanics & Shear modulus.

Summary

1. Introduction

• Fatigue cracking in bituminous binders is one of the most major distresses resulting in the degradation of asphalt pavements.
• The fatigue cracking mechanism of the bituminous binders are not yet well understood, particularly on how the crack was initiated in the binders under a rotational shear fatigue load.
• The question (a) on what the damage is has been tentatively addressed by one of the authors' previous studies [13] .
• Using damage mechanics, a DSR-cracking (DSR-C) model was developed to predict the crack length in the bitumen sample under the rotational shear fatigue load [13] .

2.1 Materials

• The 40/60 bitumen, base X-70 bitumen and 100/150 bitumen are unmodified binders with different penetration grades and the X-70 bitumen is a polymer-modified binder with 45/80 penetration grade.
• These binders were all aged using standard methods including Rolling Thin Film Oven (RTFO) for short-term ageing [37] and Pressure Ageing Vessel (PAV) for long-term ageing [38] .
• Laboratory tests including contact angle measurements and Dynamic Shear Rheometer (DSR) tests were conducted on eight samples, i.e., unaged 40/60 bitumen, RTFO aged 40/60 bitumen, PAV aged 40/60 bitumen, unaged X-70 bitumen, RTFO aged X-70 bitumen, PAV aged X-70 bitumen, PAV aged base X-70 bitumen and PAV aged 100/150 bitumen.

2.2 Contact angle measurements

• In order to determine surface energy of the bituminous binders, contact angle measurements were performed using Sessile Drop method.
• The selection of probe liquids is critical for the contact angle measurements using the Sessile Drop method.
• Their surface energy components must be known to determine the surface energy of bituminous binders.
• The glass slide coated with the bitumen was first placed between the light source and the camera of the test device.
• An image of the drop was captured by the camera and then the captured image was analysed automatically by image processing software of the test device to obtain the angle between the baseline and the edge of the drop.

2.3 Dynamic Shear Rheometer (DSR) tests

• To determine the linear viscoelastic properties and fatigue cracking behaviours of the bituminous binders, viscoelastic frequency sweep tests and time sweep fatigue tests were performed on all binders in this study.
• Bitumen samples were prepared for the tests using silicone moulds and all the tests were conducted using a Kinexus DSR from Malvern Panalytical with an 8 mm parallel plates with 2 mm gap as the sample height.
• Two replicates were tested for each testing condition and one more replicate was required when their deviation was more than 10%.
• To eliminate the effects of the initial stiffness of the bituminous binders, a fixed iso-.
• To study the fatigue cracking behaviours of the binders, time sweep fatigue tests were performed at the iso-stiffness temperature and the frequency of 10 Hz under a 5% shear strain level corresponding to the rotation amplitudes of 0.025 rad.

3. Viscoelastic characterisation of bituminous binders with pseudostrain

• When a viscoelastic material is subjected to a rotational shear fatigue load, its stress- strain curve forms a hysteresis loop in each load cycle.
• The area inside the loop is the dissipated energy (DSE) density and the area between the stress- curve and the horizontal axis is defined as the recoverable energy (RSE) density.
• After introducing pseudostrain, the stress-pseudostrain curve at the linear viscoelastic state becomes a straight line, which indicates that the viscous effect is eliminated and the stress-pseudostrain shows like an elastic behaviour.
• The maximum RPSE occurs at the location where the radius is the maximum which is the edge of the sample.

4.1 Crack initiation of bituminous binders under a rotational shear fatigue load

• Under a rotational shear fatigue load, the crack in a cylindrical bitumen sample grows as a circumferential crack that initiates at the edge of the sample and propagates toward the centre [13, 14] .
• Based on the DSR-C model shown in Eq. ( 9) [13] , the crack growth in bituminous binders under a rotational shear fatigue load can be predicted using the moduli and phase angles of the binders in the undamaged and damaged conditions.
• It can be seen from Figs. 4 and 5 that the crack length has a sharp increase and the crack growth rate shows a significant fluctuation.
• A sequence of processes occurring in this stage are described as follows: (1) Molecular rearrangements.
• Due to the edge instability and geometry dependence of samples, it becomes very challenging to develop a rigorous model or theory to characterise the molecular rearrangements or the microcrack nucleation during the edge flow damage.

4.2 Energy redistribution due to 'factory-roof' cracking

• According to the cracking pattern of bitumen binders under the rotational shear fatigue load shown in Figs.
• Note that the edge flow damage zone was removed from the calculation of the total V as no RPSE was stored in the zone due to the edge flow damage in the sample.
• The horizontal height of the triangular region is the crack length a and the vertical height of the triangular region is ka according to the previous study [52] .
• Thus, the volume for releasing RPSE can be expressed as EQUATION ).

4.3 Crack initiation criterion

• The Griffith crack initiation criterion states that the potential energy of an elastic body remains unchanged when cracks initiate or the existing cracks grow.
• Thus, the crack initiation follows an energy balance condition, where the rate of total energy to crack size equals to zero.
• Based on this criterion, the critical condition at the moment when the crack is initiated can be expressed as EQUATION ) where ε is the total pseudostrain energy after the energy redistribution in the sample shown in Eq. ( 10).
• It is noted that, in Eq. ( 16), the recoverable pseudostrain energy density RPSE(r) is related to the shear modulus of materials and the loading amplitude (see Eq. ( 8)).

5.1 Surface energy of bituminous binders

• To predict the acid-base interaction, the acid-base term in Eq. ( 17) was divided into a Lewis acid component and a Lewis base component, as described in Eq. ( 18).
• The surface energy components of the bituminous binders were determined indirectly using contact angle measurements in this study.
• Table 4 shows the total surface energy of the tested binders with their surface energy components.

5.2 Determination of model parameters

• To implement the energy-based crack initiation criterion for the bitumen in Eq. ( 16), the model parameters are discussed and determined in this section.
• The recoverable pseudostrain energy density RPSE(r) is calculated using Eq. ( 8 G . The authors' previous study [45] proved that, when assigning the material modulus to the reference modulus, the physical meaning of the pseudostrain becomes the difference between the viscous strain and the total strain.
• It is noted that some studies [55, 56] used a unit (1 Pa) as the reference modulus, however, this will result in an unclear physical meaning of the pseudostrain as the unit reference modulus has normalised the pseudostrain when the stress-pseudostrain relations are modelled.
• The surface energy Γ was calculated based on the contact angle measurements that have been presented in Section 5.1.
• The edge flow damage size 0 c was determined as the corresponding crack length at which the minimum crack growth rate was obtained before the "factory-roof" crack propagation is started in the TS tests, as shown in Fig.

5.3 Validation of crack initiation criterion

• To validate the crack initiation criterion, Eq. ( 16) is used to predict the surface energy of the bitumen.
• Closer the data points are to the quality line, smaller the difference between the predicted and measured values is.
• The difference ratio R is also calculated to show a measure of how close the data are to the quality line.
• The average R for all tested samples is 7.51%, which means that the predicted results agree well with the tested data.
• Furthermore, it is concluded that the crack initiation criterion can be used to determine the surface energy of the bituminous binders by the DSR fatigue tests.

5.4 Crack initiation analysis of bituminous binders

• After validation, the fatigue crack initiation of bituminous binders can be analysed using the developed energy-based criterion.
• According to these experimental results, the fatigue cracking process in the bituminous binders is analysed and discussed to reveal the cracking mechanism and thus to model the fatigue crack initiation illustrated in Fig. 6 .
• For both the 40/60 and X-70 binders, the number of load cycles grows as the ageing level increases.
• It has been reported by the authors' previous study [15] that the ageing accelerates the crack propagation and reduce the fatigue crack propagation life.
• Among the four kinds of PAV aged binders (i.e., PAV 40/60, PAV X-70, PAV base X-70, PAV 100/150), the number of load cycles for the polymer-modified X-70 bitumen is the largest (4314), which demonstrates that the polymer modification can improve the binder resistance to the crack initiation and extend the fatigue crack initiation life.

5.5 Potential application of crack initiation criterion

• This energy-based criterion can be potentially applied to determine the critical shear stress for the crack initiation of bituminous binders subjected to the rotational shear fatigue loads.
• Substituting Eq. ( 22) into Eq. ( 16) and then considering 0 0 G is the energy release ratio (surface energy of the crack for brittle materials).
• Similarly, the critical shear strain can be expressed as EQUATION.
• The critical shear stress (Eq. ( 23)) or strain (Eq. ( 25)) identifies the critical condition when the crack initiation occurs in the bituminous binders subjected to the rotational shear fatigue loads.
• The critical condition for crack initiation is called the endurance limit, which is the maximum amplitude of a cyclic load applied to a material that does not lead to fatigue failure of the material.

6. Conclusions

• An energy-based crack initiation criterion is developed for the bituminous binders subjected to a rotational shear fatigue load based on mechanics principles and physical facts during the crack initiation process.
• Laboratory tests including contact angle measurements and DSR tests are conducted to determine the model parameters.
• (3) The local energy redistribution due to the circumferential 'factory-roof' crack is quantified by the pseudostrain energy.
• A crack initiation criterion is developed for bitumen under a rotational shear fatigue load based on viscoelastic Griffith's fracture mechanics.
• (4) The crack initiation is dependent of the shear modulus and surface energy of bituminous binders, critical crack size, and loading amplitude.

Figures

Table 1 Surface energy components of probe liquids (mJ/m2). 171

Fig. 1. Bitumen samples and test instrument used for contact angle measurements. (a) Glass 189 slide samples. (b) Tensiometer from Biolin Scientific. 190 191 192 193 194

Fig. 4. Crack growth with the number of load cycles for a cylindrical bitumen sample subjected 331 to a rotational shear fatigue load. 332 333

Table 2 Contact angles between tested bitumen and liquid probes (°). 195

Table 5 Predicted results of fatigue crack initiation for all tested bituminous binders using 581 developed energy-based crack initiation criterion. 582

Table 3 Iso-stiffness temperature for all the tested bitumens. 219

Table 4 Surface energy components of tested bitumens (mJ/m2). 484