{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T06:46:36Z","timestamp":1776581196177,"version":"3.51.2"},"reference-count":52,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T00:00:00Z","timestamp":1740614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"U.S. Department of Energy (DOE) Laboratory Directed Research and Development (LDRD)","award":["#2024-00146"],"award-info":[{"award-number":["#2024-00146"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The crack tip opening angle (CTOA) is one of fracture toughness parameters that has been used for decades in describing large stable crack growth in thin-walled aerospace structures under the low-constraint conditions. Recently, the pipeline industry has developed a growing interest in using the CTOA parameter to serve as the minimum required fracture toughness to arrest dynamic crack propagation in modern gas transmission pipelines made of high-strength ductile steel. To meet this industrial need, the CTOA test standard ASTM E3039 was therefore developed for measuring the constant critical CTOA. ASTM E3039 recommends a drop weight tearing test (DWTT) specimen with a shallow crack for standard CTOA testing, but its CTOA may depend on the low constraint condition of the DWTT specimen at the crack tip. Verifying the constraint independence of the DWTT-measured CTOA thus becomes indispensable for applying CTOA toughness to the running fracture control in the pipeline design. For this purpose, the present paper evaluates critical CTOA values in a set of fracture toughness tests on single-edge notched bend (SENB) specimens with shallow and deep cracks, based on four CTOA estimation models. Among these, the Ln(P)-LLD linear fit model is similar to that recommended by ASTM E3039 for CTOA calculation. Fracture test data for X80 pipeline steel and HY80 structural steel were considered in the CTOA evaluation. The results showed that the four CTOA models were able to determine a constraint independent CTOA value for stable crack growth in the SENB specimens. As a result, a single, reliable, constant CTOA value could be determined regardless of the specimen geometry or the crack-tip constraint conditions. Therefore, the CTOA measured using ASTM E3039 is constraint-independent and transferable to use in cases of actual cracks propagating in gas transmission pipelines.<\/jats:p>","DOI":"10.3390\/ma18051051","type":"journal-article","created":{"date-parts":[[2025,2,27]],"date-time":"2025-02-27T03:37:57Z","timestamp":1740627477000},"page":"1051","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Determination of Constraint-Independent Crack Tip Opening Angle for Stable Crack Growth in High-Strength Ductile Steels"],"prefix":"10.3390","volume":"18","author":[{"given":"Xian-Kui","family":"Zhu","sequence":"first","affiliation":[{"name":"Materials Technology and Energy Science, Savannah River National Laboratory, Aiken, SC 29808, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1115\/1.3601206","article-title":"A path independent integral and the approximate analysis of strain concentration by notches and cracks","volume":"35","author":"Rice","year":"1968","journal-title":"J. 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