# Fatigue Life Prediction of High Modulus Asphalt Concrete Based on the Local Stress-Strain Method
## 9 Conclusions  
This study provides an experimental investigation into the fatigue performance of high modulus asphalt concretes, including the cyclic \(\sigma-\varepsilon\) test and direct tensile fatigue test. A method to predict the fatigue crack initiation life of HMAC was proposed based on the modified Neuber equation and local \(\sigma-\varepsilon\) method. The following conclusions can be drawn based on this work:  
1. The cyclic \(\sigma-\varepsilon\) curve and modified \(\sigma-\varepsilon\) curve of HMAC in plane strain state were established.
2. Conversion from nominal stress and strain to local strain-stress is proposed based on a modified Neuber equation and the local stress-strain method.
3. The strain fatigue equation for HMAC is presented based on fatigue tests.
4. The fatigue life model is able to produce satisfactory crack initiation life predictions using the local stress-strain method based on fatigue test analysis of the specimens and the modified Neuber equation.  
**Acknowledgments:** The research was sponsored by the National Natural Science Foundation (Grant No. 51008033), the Fundamental Research Funds for the Central Universities (Grant No. 310821163502), the Transportation Department of Shandong Province (Grant No. 2008Y007), the Transportation Department of Hainan Province (Grant No. 201000005), and the Transportation Department of Hubei Province of China (Grant No. Ejiaokejiao [2013] 731).  
**Author Contributions:** Professor [PERSON] was in charge of the whole research plan and paper submission matters. The first author extends gratitude to [PERSON], [PERSON] and [PERSON] for performing the experiment and analyzing test data, to [PERSON] and [PERSON] for offering help in doing the experiment.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**List of Symbols**  
\(\varepsilon_{a}=\) strain, \(\Delta\varepsilon=\) cyclic strain amplitude, \(\Delta\varepsilon_{\rm e}=\) circular elastic, \(\Delta\varepsilon_{p}=\) plastic strain amplitude, \(\sigma^{\prime}{}_{f}=\) fatigue strength coefficient, \(\varepsilon^{\prime}{}_{f}=\) ductility coefficient, \(N_{f}=\) fatigue life, \(b\), \(c=\) regression constants, \(\varepsilon_{\rm ea}=\) elastic strain, \(\varepsilon_{\rm pa}=\) plastic strain, \(K_{t}=\) theoretical stress concentration factor of notch, \(K_{e}=\) strain concentration factors, \(K_{e}=\) factor of stress concentration, \(e=\) nominal strain, \(S=\) nominal stress, \(K_{f}=\) fatigue notch factor, \(M=\) plastic penetrable degree, \(g=\) coefficient of equivalent stress and strain, \(\mu^{\prime}=\) elastic-plastic Poisson's ration, considering the compressibility of material, \(\mu=\) Poisson's ration, \(E=\) elasticity modulus, \(E_{s}=\) secant modulus, determined by the monotone tensile curve.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Axle Load/kN** & **80** & **100** & **120** & **150** & **180** \\ \hline Local strain & 1.2892 & 1.4009 & 1.4432 & 1.5057 & 1.5965 \\ Calculated loading times & 79,547 & 55,698 & 15,634 & 9846 & 5765 \\ Statistics of traffic loading times & 627 & 2568 & 1931 & 122 & 70 \\ Fatigue damage & 0.0079 & 0.0461 & 0.1235 & 0.0124 & 0.0121 \\ \hline \hline \end{tabular}
\end{table}
Table 14: The analysis of fatigue damage.