This study presents a three-dimensional global–local formulation for the prediction of guided wave scattering from discontinuities (e.g. defects). The approach chosen utilizes the Semi-Analytical Finite Element method for the “global” portion of the waveguide, and a full Finite Element discretization for the “local” portion of the waveguide containing the discontinuity. The application of interest is the study of guided wave scattering from transverse head defects in rails. Theoretical scattering results are impossible to obtain in this case for a wide-frequency range. While three-dimensional Semi-Analytical Finite Element–Finite Element models for guided wave scattering studies have been used in the past, this is the only study where guided waves in rails were modeled in a wide-frequency range (up to 180 kHz). A comparison analysis with a benchmark study of wave reflections from the free end of a cylindrical rod is conducted first. For the case of the rail, selected case studies of incoming guided modes were chosen, and reflection and transmission spectra are calculated for head defects of various sizes. This kind of results can be utilized to guide and/or interpret ultrasonic guided wave tests aimed at defect detection or quantification. Finally, parametric studies are conducted to examine more closely the role of certain operational parameters that are important in this kind of analysis, and specifically the size of the “local” region and the number of guided modes considered. These parametric studies lead to compromises that need to be struck on the basis of conservation of energy among all wave modes involved.

这项研究提出了一种三维全局局部公式，用于预测来自不连续性（例如缺陷）的导波散射。选择的方法对波导的“整体”部分使用了半解析有限元方法，对包含不连续性的波导的“局部”部分使用了完整的有限元离散化。感兴趣的应用是研究钢轨中横向头部缺陷引起的导波散射。在这种情况下，无法在较宽的频率范围内获得理论上的散射结果。过去曾使用三维半解析有限元-有限元模型进行导波散射研究，但这是唯一在宽频率范围（高达180 kHz）中对导轨中的导波进行建模的研究。首先进行比较分析和基准研究，以研究圆柱棒自由端的波反射情况。对于铁路的情况，选择了进入的引导模式的选定案例研究，并计算了各种尺寸的头部缺陷的反射和透射光谱。这种结果可用于指导和/或解释针对缺陷检测或定量的超声导波测试。最后，进行参数研究以更仔细地检查某些操作参数在此类分析中的作用，尤其是“局部”区域的大小和所考虑的引导模式的数量。这些参数研究导致折衷，需要在所有涉及的波模之间的能量守恒的基础上进行折衷。