Fatigue Test Modes and Loading Configuration

Asphalt fatigue tests are carried out using two modes, either a constant applied load (controlled stress) or constant displacement (controlled strain). With controlled stress, the stress amplitude is kept constant and the strain response increases during the fatigue test. In contrast, a constant strain is maintained in the controlled strain mode and the stress response decreases during the test, as illustrated in Figures 2–4 and 2–5. The controlled stress test mode is generally applicable to thick asphalt pavement layers, usually thicker than 200 mm, where high stiffness is the fundamental parameter used to assess the fatigue life; in contrast, the controlled strain test mode is considered to be more suitable for thin asphalt pavement layers, usually thinner than 50 mm, where the elastic properties of the materials have a fundamental impact on the fatigue life (Pell 1973, Thom 2008, Yu 2013).

Additionally, fatigue life in terms of number of cycles is longer in the controlled strain test than in the controlled stress test (Branco 2008). This can be explained based on Paris’ law for modelling crack propagation in Equation 2–1 (Paris and Erdogan 1963), where the crack length (г) is a function of stress intensity factor (K) and material properties (a, b); also, K is a function of stress (σ) and (г) in addition to specimen geometry factor (Ω), as shown in Equation 2–2.

PhD Thesis Page 16 𝑑Γ

𝑑𝑁= 𝑎(∆𝐾)^𝑏 (2–1) 𝐾 = Ω𝜎√𝜋Γ (2–2)

Figure 2-4: Controlled stress test mode.

Figure 2-5: Controlled strain test mode.

It is clear that the crack propagation basically depends on the stress intensity, and stress intensity decreases in the controlled strain test mode because the stress decreases as the fatigue test progresses, and it is sometimes below a value at which the material can withstand this damage to continue to a high or infinite number of cycles, which is sometimes called the endurance limit (Bhattacharjee et al. 2009, Witczak et al. 2013). In contrast, the stress intensity is constant along the test in the controlled stress test mode, and the materials with crack propagation become weaker and quicker to damage. Thus, if we proposed that the test in both

Strain amplitude

Time (sec)

Strain response

Time (sec)

Stress amplitude

Time (sec)

Stress response

Time (sec)

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modes starts at the same stress intensity, the fatigue life as a number of cycles in the strain mode is definitely longer than the stress mode under the same test conditions.

In the fatigue test there are two main configurations of loading, either haversine waveform (ASTM D7460-2008) or sinusoidal waveform (AASHTO T321-2007), as well as British Standards (BS EN 12697-24 2012). The main difference between the two configurations is that the load in a haversine waveform bends the beam downward in one direction, while in a sinusoidal waveform the load bends the beam in both upward and downward directions with half the magnitude of the haversine waveform, as shown in Figure 2–6. Typically, this can be characterised by the ratio (R), which is the ratio of the minimum force or displacement to the maximum force or displacement; thus, a pure sinusoidal waveform is characterised by R=-1 while R=0 for a haversine waveform.

Figure 2- 6: Bending direction for both configurations of loading (a) sinusoidal and (b) haversine.

It is clear that stress and strain in sinusoidal loading follow the sinusoidal waveform throughout the fatigue test, as shown in Figure 2–7; also, the neutral position of the beam remains in the same position, halfway between the extreme positions, as shown in Figure 2–6a. In contrast, in the haversine waveform stress, strain and deflection follow the haversine waveform during the first cycles; as the test progresses, the behaviour changes from haversine to sinusoidal waveform for

(a) Sinusiodal (AASHTO T321)

extreme positions neutral position

(b) Haversine (ASTM D-7460)

extreme postion neutral positions extreme positions

First cycles During test

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strain and stress while the deflection remains haversine waveform, as detailed in Figure 2–8. Therefore, an initial permanent deformation (creep) occurs during the first cycles due to the viscose character as a relaxation response of the beam during the loading/unloading within the initial cycles, where the stress builds up because of the HMA’s nature but then relaxes because of its ability to undergo viscous flow. During this process, the neutral position moves downward, which is located halfway between the extreme positions, as shown in Figure 2–6b.

Figure 2- 7: Stress and strain vs time for sinusoidal waveform loading (BS EN 12697-24 and AASHTO T321).

Additionally, the R value of the haversine waveform during cyclic loading is not the same as at the beginning, i.e. R=0, (Pronk and Erkens 2002). The stress and strain signals change into a sinusoidal form in strain test modes and the R factor will change from 0 to -1; also, a new neutral axis for the beam will be created because of the permanent deformation (creep), as shown in Figure 2–6b, and this axis continues to the end of the test, so at the end of the test the beam has been bent. However, the deflection form remains haversine along the test, as shown in Figure 2–8. In stress mode, immediately after creating the permanent deformation, the stress-strain signals convert into a sinusoidal form (R=-1) but there is an increasing R factor (R>0) in the deflection signal. This is because the load is not influenced by the permanent deformation, and the beam is subjected to the same load as in the undamaged specimen, causing progressive curvature of the beam

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due to the cumulative permanent deformation; thus, the neutral axis is changing as loading progresses. Thus, the haversine loading form comprises two types of damage to components: fatigue damage and creep damage, but creep damage in the stress mode is more than in the strain mode as a result of the increased permanent deformation (creep) (Pronk and Erkens 2002).

Figure 2- 8: Stress, strain and deflection vs time for haversine waveform loading (ASTM D-7460).

The developed stress and strain during sinusoidal loading generate reversible tension and compression on the top and bottom of the beam during cyclic loading.

In contrast, the movement to one direction in haversine loading creates tension at

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the bottom and comparison on the top of the beam during the first cyclic loading;

later the developed stress and strain change to sinusoidal waveform, causing changeable tension and comparison with half stress magnitude at the beginning of the test. So, at the end of the haversine test and after removing the loading the sample remains bent downward while in sinusoidal loading the sample remains straight (Pronk et al., 2010;Witczak et al., 2013).

Mamlouk et al. (2012) revealed that the haversine loading gave unexpected results in a healing study in compression with sinusoidal waveform loading. Whereas the fatigue life with rest period in haversine loading was shorter than without rest period and this result was unexpected, in contrast, fatigue life in sinusoidal waveform loading produced consistent and expected results (Mamlouk et al., 2012). This effect was justified in the same study (Mamlouk et al., 2012); where, the developing stress and strain during sinusoidal loading with and without rest period creates reversible tension and compression to the top and bottom of the beam. In contrast, the haversine waveform loading with rest period is more harmful where it creates higher tension stress because the beam being bent double time than sinusoidal, consequently high tension at the bottom of the beam is generated. As is known, tension stress reduces fatigue life while compression stress helps to heal the micro cracks to extend fatigue life. So, the recommendation of this study was adopting sinusoidal waveform AASHTO T-321 in studying the healing instead of haversine. While in ASTM D7460 haversine was used because the loading shape is similar to the nature of loading on the pavement surface (Pronk et al., 2010).