Abstract Six constraint parameters (namely T-stress, Q, h, Tz, Ad and Ap) have been numerically calculated for semi-elliptical surface cracks in pipes so as to comparatively investigate their capability, applicability and ease of use for characterizing in-plane and out-of-plane constraints. The results show that the parameters T-stress and Tz can separately characterize in-plane and out-of-plane constraints. The crack depth a/t and aspect ratio a/c of semi-elliptical cracks can influence both in-plane and out-of-plane constraints. With decreasing a/c (increasing crack length) and increasing crack depth a/t, both in-plane and out-of-plane constraints increase. The parameters Q and stress triaxiality factor h are equivalent, and they can capture both in-plane and out-of-plane constraints for the cracks in pipes. But they may overestimate constraint for longer cracks with lower a/c. The parameters Ad and Ap based on crack-tip plastic deformation (or strain) can equivalently characterize both in-plane and out-of-plane constraints for the cracks in pipes. The advantages and limitations of different constraint parameters in terms of their engineering applications are analyzed and appropriate parameters are recommended.

中文翻译：

---

管道半椭圆表面裂纹不同约束参数的面内和面外约束表征

摘要 对管道半椭圆形表面裂纹6个约束参数（即T-stress、Q、h、Tz、Ad和Ap）进行数值计算，比较研究它们表征面内裂纹的能力、适用性和易用性。和平面外约束。结果表明，参数T-stress和Tz可以分别表征面内和面外约束。半椭圆裂纹的裂纹深度 a/t 和纵横比 a/c 会影响面内和面外约束。随着 a/c（增加裂纹长度）和增加裂纹深度 a/t，平面内和平面外约束都增加。参数 Q 和应力三轴系数 h 是等效的，它们可以捕获管道裂纹的平面内和平面外约束。但是他们可能会高估对空调较低的较长裂缝的约束。基于裂纹尖端塑性变形（或应变）的参数 Ad 和 Ap 可以等效地表征管道裂纹的平面内和平面外约束。分析了不同约束参数在工程应用中的优缺点，并推荐了合适的参数。