Elastic‐Shakedown‐Informed Tensor‐History‐Based Critical‐Plane Fatigue Assessment Under Proportional Loading

Fatigue assessment of notched components remains difficult when local yielding, residual‐stress‐biased tensor histories, and critical‐plane damage metrics interact. This study develops an elastic‐shakedown‐informed tensor‐history workflow combining finite‐cycle numerical shakedown screening, stabilized Ramberg–Osgood material input, MRVD critical‐plane scanning, and an MCPES fatigue parameter. The workflow is benchmarked using published 34CrNiMo6 lateral U‐notch fatigue data; six candidate cases are screened and four cases satisfying the adopted finite‐cycle numerical shakedown‐screening criterion are retained for route comparison. The retained cases show case‐dependent agreement among nominal‐stress, pure‐elastic, Neuber–SWT, and shakedown‐consistent tensor‐history routes, while a hydraulic‐cylinder model illustrates route sensitivity under an amplified proportional‐pressure assessment condition. The results remain limited to the screened proportional‐loading cases and do not establish long‐term instability or experimentally verified component life. Accordingly, the study is presented as a finite‐cycle, path‐dependent mechanistic and numerical route‐comparison sensitivity study rather than a generally validated fatigue‐life framework.