This work investigates the effect of the notch on fatigue behavior by combining two methods: the extended finite element method (XFEM) and the averaged strain energy density (ASED) method, which considers the combined action of bending and shear loading. The ASED method has already been proven accurate for assessing the failure of components in the presence of sharp and blunt notches, and several results are available in the literature for different materials. These results were compared with those obtained from the experimental tests reported here. The main purpose of this study was twofold: The first part is an experimental study of fatigue in rotary bending of specimens weakened by U and V notches made of polymethyl-methacrylate (PMMA) material. Two values for the radius were used for the U-notches (0.2 and 2 mm) and two angles for the V-notches (20° and 140°). The second part of the study consisted of performing several simulation tests using the Cast3m software for different angles and radii. The local approach based on the mean value of the ASED acted over a finite-sized volume surrounding the highly stressed regions. The maximum principal stress located at the notch edge defined the center of the control volume. If the notch is blunt, the control volume assumes a crescent shape with its width measured along the notch bisector line. When the notch is considered pointed (V-notched) or is a crack, the control volume becomes a circle with its center at the notch tip. The presence of geometric discontinuities in structures affects their lifetime by reducing it, producing a high concentration of local energy around the notch tip. Good convergence was obtained between the numerical simulation and experimental results for the ASED in a finished zone surrounding the notch tip.

中文翻译：

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基于应变能密度法和扩展有限元法的缺口效应对聚甲基丙烯酸甲酯金属疲劳行为的数值与实验分析

这项工作结合两种方法研究了缺口对疲劳行为的影响：扩展有限元法（XFEM）和平均应变能密度（ASED）法，考虑了弯曲和剪切载荷的联合作用。ASED 方法已被证明可以准确地评估存在尖锐和钝凹口的部件的故障，并且文献中提供了针对不同材料的多个结果。将这些结果与从此处报告的实验测试中获得的结果进行比较。这项研究的主要目的有两个：第一部分是对聚甲基丙烯酸甲酯 (PMMA) 材料制成的 U 型和 V 型凹口削弱的样品旋转弯曲疲劳的实验研究。U 形凹口使用两个半径值（0.2 和 2 毫米），V 形凹口使用两个角度（20° 和 140°）。研究的第二部分包括使用 Cast3m 软件针对不同角度和半径进行多次模拟测试。基于 ASED 平均值的局部方法作用于高应力区域周围的有限尺寸体积。位于凹口边缘的最大主应力定义了控制体积的中心。如果凹口是钝的，则控制体积呈现新月形状，其宽度沿着凹口平分线测量。当凹口被认为是尖的（V 形凹口）或者是裂纹时，控制体积变成一个圆，其中心位于凹口尖端。结构中几何不连续性的存在会通过减少几何不连续性来影响其寿命，从而在凹口尖端周围产生高度集中的局部能量。ASED 在凹口尖端周围的成品区域中的数值模拟和实验结果之间获得了良好的收敛性。