Abstract In this work, the evolution of crack lengths under fatigue load is interpreted as a sample function of a cumulative damage process which, once normalized, allows a phenomenological model to be satisfactory applied using cumulative distribution functions (cdfs) of the generalized extreme value family (GEV). The denoted “retroextrapolation” procedure is used to determine the complete evolution of the a-N crack growth curve from the final fragment of the curve recorded during the test implying the consideration of additional crack growth phases, namely, prior to the pre-crack length and subsequent to the failure, respectively. The proposed methodology verifies excellent fitting of the a-N curves. It also ensures its conversion to fatigue crack growth rate curves (CGR) and, as a result, promotes the analysis of the transition from micro- to macrocracks, depending on the resulting parameters for the material tested, the specimen geometry and test type. Lastly, it allows a probabilistic analysis on the prediction of fatigue life originated from random initial sizes of cracks, smaller or larger than those induced in the experimental program to determine the a-N curve. In this way, a statistically reliable basis is provided for the application of the damage tolerance concept to the practical component design.

中文翻译：

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使用基于广义极值族累积分布函数的现象学模型逆推裂纹扩展曲线

摘要 在这项工作中，疲劳载荷下裂纹长度的演变被解释为累积损伤过程的样本函数，一旦归一化，就可以使用广义极值族的累积分布函数 (cdfs) 来令人满意地应用现象学模型。 (GEV)。所表示的“逆外推”程序用于确定 aN 裂纹扩展曲线从测试期间记录的曲线的最终片段的完整演变，这意味着考虑额外的裂纹扩展阶段，即在预裂纹长度之前和随后的到失败，分别。所提出的方法验证了 aN 曲线的出色拟合。它还确保将其转换为疲劳裂纹扩展速率曲线 (CGR)，因此，根据测试材料的结果参数、试样几何形状和测试类型，促进从微观裂纹到宏观裂纹的转变分析。最后，它允许对源自随机初始裂纹尺寸的疲劳寿命预测进行概率分析，裂纹的初始尺寸小于或大于确定 aN 曲线的实验程序中诱导的裂纹。通过这种方式，为将损伤容限概念应用于实际部件设计提供了统计上可靠的基础。