A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect.

提出了一种考虑变幅加载条件下加载序列效应的修正疲劳损伤模型。过渡序列是通过等效雨流计数方法从计数序列中获得的，用于为疲劳损伤累积预测提供加载序列信息。在雨流计数序列和转移序列的基础上，制定了雨流计数矩阵和序列转移矩阵。详细评估了两个矩阵和原始加载顺序之间的关系。在确定性疲劳估计中，雨流计数矩阵和序列转移矩阵被整合到提出的基于线性损伤规则的修正损伤模型中。平均应力转换应用于雨流计数矩阵以获取载荷水平效应。现有的实验数据用于验证确定性框架的疲劳损伤估计。为了评估随机加载条件下的疲劳，将雨流计数矩阵和序列转移矩阵映射到基于平稳随机过程的一维指数和拉普拉斯分布。进行数值模拟以验证所提出的映射分布。同时，还研究了相关长度对平稳随机加载序列下所提出分布的影响。最后，利用给定的雨流计数矩阵和序列转移矩阵的分布，模拟并讨论了用于概率疲劳估计的重建过程。所提出的模型提供了对具有序列转换效果的原始加载序列的复杂近似。所提出的修正疲劳损伤模型利用来自最初施加的载荷的足够序列信息来纠正线性损伤规则的缺陷。此外，概率疲劳估计可以评估具有序列过渡效应的随机加载过程下的累积疲劳损伤。