Accurate fatigue lifetime prediction is a central element in many industries. Often, a damage tolerant approach is used to ensure that some given imperfections are safe. In this context, these lifetime predictions are frequently made using simplified crack geometries leading to costly conservatism. In particular for a closed crack front, a circular or elliptical crack enclosing the real defect is generally used leading to an underestimation of the real lifetime. Using an iterative perturbation method to simulate the fatigue growth of many tensile complexly shaped cracks, we show that in the absence of any additional complexity, (i) the front quickly becomes circular; (ii) its evolution with the number of loading cycles can be obtained analytically using a circular crack of same area as the original distorted defect. In practice, it means that replacing a complex crack front shape with this simple, analytically solvable configuration is an effective way to improve predictions and that it is not useful to invoke more complex shapes such as elliptical cracks. These take-home messages are illustrated by an example from the aviation industry.

准确的疲劳寿命预测是许多行业的核心要素。通常，使用损坏容忍方法来确保某些给定的缺陷是安全的。在这种情况下，这些寿命预测经常使用简化的裂纹几何形状进行，从而导致代价高昂的保守主义。特别是对于闭合裂纹前沿，通常使用包围真实缺陷的圆形或椭圆形裂纹导致对真实寿命的低估。使用迭代扰动方法来模拟许多拉伸复杂形状裂纹的疲劳增长，我们表明，在没有任何额外复杂性的情况下，（i）前端迅速变成圆形；(ii) 可以使用与原始变形缺陷相同面积的圆形裂纹分析获得其随加载循环次数的演变。在实践中，这意味着用这种简单的、可解析求解的配置替换复杂的裂纹前沿形状是改进预测的有效方法，而调用更复杂的形状（如椭圆形裂纹）则没有用。航空业的一个例子说明了这些带回家的信息。