## 1 Introduction  
The failure of most engineering structures or mechanical parts is caused by the accumulation of fatigue damage caused by a series of cyclic loads. Factors affecting the accumulation of fatigue damage include load size, loading sequence, load history (number of actions), and load path. The cumulative effect of fatigue damage directly determines the life and reliability of mechanical parts. Scholars have done a lot of work in the field of fatigue cumulative damage and have proposed many fatigue cumulative damage theories and calculation models, which are mainly divided into linear fatigue cumulative damage theory, bilinear cumulative damage theory, and nonlinear fatigue cumulative damage theory [1]. The commonly used linear fatigue cumulative damage theory [2] (Miner's rule) does not consider the influence of the load sequence, but the fact that [PERSON]'s rule ignores the effects of load sequence and load interaction make lifetime estimations obtained by this rule unsatisfactory [3, 4]. Although the bilinear cumulative damage theory considers the effect of load sequence on crack growth to a certain extent, its theoretical model cannot accurately simulate the actual damage process because it is difficult to determine the inflection point of crack growth. Therefore, the accuracy of life prediction is not high [5, 6]. For the strain control of austenitic stainless steel, [PERSON] [7] proposed a conservative model of fatigue damage accumulation under variable amplitude load. This model does not require the constitutive law but considers plasticity through the cyclic strain stress curve. In order to overcome the shortcomings of the linear damage accumulation Miner's rule, a wide range of nonlinear damage accumulation models have been developed. According to the change characteristics of fatigue ductility, and based on the theory of continuum damage mechanics, [PERSON] [8] proposed a modified nonlinear uniaxial fatigue damage accumulation model. The model could be used to predict the failure of the specimen and explain the whole process of fatigue damage accumulation. [PERSON] [9] developed a practical and simple correction factor ensuring that the linear summation of damage was conservative, so as to take the sequence effect into account in random loading. Nonlinear fatigue cumulative damage theory believes that the load sequence has a serious impact on fatigue cumulative damage [10; 11; 12; 13]. Although these models are often capable of producing satisfying results for a specific set of experiments, Miner's rule remains the most widely used for fatigue design under variable amplitude loading. However, some models have recently been developed, which do not require extensive testing. Many fatigue damage accumulation theories have been proposed to remedy the drawbacks of [PERSON]'s rule, and a majority of these models are based on non-linear accumulation laws. [PERSON] [14] proposed a method for the prediction of the fatigue-life for different materials subjected to constant amplitude multiaxial proportional loading. The non-linear fatigue damage accumulation models can be classified into the following categories: damage curve based models, continuum damage mechanics models, interaction between the various loadings considered models, energy-based damage methods, physical properties degradation-based models, ductility exhaustion-based methods, thermodynamic entropy-based damage theories. Detailed comments on some of these models can be found in [15]. Based on the fatigue test data of the high-low loading and low-high loading of 18 CrNiMo7-6 steel, an improved nonlinear cumulative fatigue damage model is proposed based on the ductile dissipation model in the nonlinear cumulative damage theory. By analyzing the damage model, the load interaction parameters can be obtained and added to the ductile dissipation model, and the value of the parameter is determined through the experimental data. This paper explains from the mechanism why Miner's rule has different damages under two-level loading.