{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T02:56:50Z","timestamp":1791082610569,"version":"4.1.0"},"reference-count":30,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Office of Naval Research","award":["N000142412177"],"award-info":[{"award-number":["N000142412177"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>In this article, we discuss an unusual pattern in long-crack behavior at low stress intensity factor ranges \u0394K (below \u0394Kth), characterized by an initial dip, followed by a plateau, and then an acceleration in fatigue crack growth (FCG) rate. This unanticipated FCG behavior was first observed experimentally in the IMI 834 alloy and reported by Marci in 1996. Such an anomaly is only reported from experimental observation but cannot be understood or explained using the plasticity, roughness, or oxide-induced crack closure assumptions. It also has not been fully explained through either metallurgical analysis or failure mode investigation. The established application of fracture mechanics to the FCG rate (da\/dN) assumes that the FCG rate decreases with decreasing \u0394K towards the threshold of \u0394Kth with (da\/dN) \u2264 10\u22127 mm\/cycle. Yet, some materials exhibit a lack of \u0394K threshold dependence for long cracks when tested using constant-Kmax or constant-R-ratio testing. An understanding of this anomaly and the related physics poses a scientific challenge. It is also relevant to predict the safe service life of structures subjected to high-frequency and low-amplitude vibrating loads. Here, we provide our interpretation and discuss the significant implications of this phenomenon in the context of damage-tolerant design.<\/jats:p>","DOI":"10.3390\/ma17246093","type":"journal-article","created":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T03:51:08Z","timestamp":1734061868000},"page":"6093","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Anomalies in Long-Crack Propagation at Low \u0394K in Some Engineering Alloys"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4760-0316","authenticated-orcid":false,"given":"Daniel","family":"Kujawski","sequence":"first","affiliation":[{"name":"Mechanical and Aerospace Engineering, Western Michigan University, Kalamazoo, MI 49008, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Asuri K.","family":"Vasudevan","sequence":"additional","affiliation":[{"name":"TDA Inc., Falls Church, VA 22043, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,13]]},"reference":[{"key":"ref_1","unstructured":"ASTM (1997). 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