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论文范文
1. Introduction Fatigue strain of the concrete can truly reflect the variation of the material deformation under the fatigue loads. If we know the relationship of the curve and the cycles, we are able to qualitatively describe the evolution of the material fatigue strain, which will provide the basis for the behavior of the material evaluation. In numerous constant amplitude fatigue tests, it is shown that the total longitude deformation and the residual deformation of the concrete will display the universal and stable three-stage law [1–6], which presents firstly the rapid growth stage, then the stable growth stage, and ultimately the rapid growth stage. This is suitable for not only the ordinary concrete, lightweight aggregate concrete, high strength concrete, or fiber reinforced concrete, but also the compression fatigue, tension fatigue, bending fatigue, uniaxial fatigue, or multiracial fatigue. Chen et al. [7] took advantage of a cubic polynomial fitting curve to get correlation coefficients above 0.937. However, different levels of stress would own different coefficients with nearly an order of magnitude. Cachim et al. [8] adopted the logarithmic form between the maximum strain rate and the load cycles in the second phase for the concrete. Under the compression fatigue loads, the form was a linear relationship. Xie et al. [9] also got an experienced index formula by fitting the second phase of fatigue strain. Wang et al. [10] fitted the data of compressive fatigue experiment strain and adopted a two-stage nonlinear formula. According to the fatigue strain evolution and methods of current analysis, the following deficiencies were discovered. ① Presently, the linear three-stage fatigue strain equations are simple, but of a low accuracy. While the three-stage nonlinear equation is of high precision, the form is complicated. It is rarely reported about the whole fatigue strain curve with the cycle ratio relationship. ② The evolution and fitting of the fatigue strain curve are aimed at a specific set of experimental data nowadays. As for the conditions that the fatigue stress is smaller than limited stress but greater than the threshold value, there are few researches. ③ A consensus has reached the variation law of the three-stage fatigue strain, and some curve fitting equations have been obtained, but the initial strain was not taken into consideration basically. In these equations, the significance of each factor is not clear enough, which results in unstable fitting coefficients. In the literature [11] published by the author, the nonlinear strain evolution model was established. The strain evolution law of concrete under constant amplitude fatigue load and the law of fatigue damage evolution based on strain were studied. Based on the previous research, in this paper, the physical meanings, the ranges, and the impact on the shape of the curve of parameters in the nonlinear strain evolution model were all discussed. The evolution model of fatigue modulus was established under constant amplitude bending fatigue loading based on the fatigue strain evolution model and the hypothesis of fatigue modulus inversely related fatigue strain amplitude. Moreover, the whole process is validated by the experimental data. 
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