{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:46:05Z","timestamp":1762051565027,"version":"build-2065373602"},"reference-count":74,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T00:00:00Z","timestamp":1653004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Spruce wood (Picea Mariana) is a highly orthotropic material whose fracture behavior in the presence of U-shaped notches and under combined tensile-tearing loading (so-called mixed-mode I\/III loading) is analyzed in this work. Thus, several tests are carried out on U-notched samples with different notch tip radii (1 mm, 2 mm, and 4 mm) under various combinations of loading modes I and III (pure mode I, pure mode III, and three mixed-mode I\/III loadings), from which both the experimental fracture loads and the fracture angles of the specimens are obtained. Because of the linear elastic behavior of the spruce wood, the point stress (PS) and mean stress (MS) methods, both being stress-based criteria, are used in combination with the Virtual Isotropic Material Concept (VIMC) for predicting the fracture loads and the fracture angles. By employing the VIMC, the spruce wood as an orthotropic material is modeled as a homogeneous and isotropic material with linear elastic behavior. The stress components required for calculating the experimental values of notch stress intensity factors are obtained by finite element (FE) analyses of the test configuration using commercial FE software from the fracture loads obtained experimentally. The discrepancies between the experimental and theoretical results of the critical notch stress intensity factors are obtained between \u221212.1% and \u221215% for the PS criterion and between \u22125.9% and \u221214.6% for the MS criterion, respectively. The discrepancies related to fracture initiation angle range from \u22121.0% to +12.1% for the PS criterion and from +1.5% to +12.2% for the MS criterion, respectively. Thus, both the PS and MS models have good accuracy when compared with the experimental data. It is also found that both failure criteria underestimate the fracture resistance of spruce wood under mixed-mode I\/III loading.<\/jats:p>","DOI":"10.3390\/ma15103661","type":"journal-article","created":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T13:56:12Z","timestamp":1653054972000},"page":"3661","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tensile-Tearing Fracture Analysis of U-Notched Spruce Samples"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4976-7080","authenticated-orcid":false,"given":"Ali Reza","family":"Torabi","sequence":"first","affiliation":[{"name":"Fracture Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran 14395-1561, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3561-9981","authenticated-orcid":false,"given":"Sobhan","family":"Mohammadi","sequence":"additional","affiliation":[{"name":"Fracture Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran 14395-1561, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Behnam","family":"Saboori","sequence":"additional","affiliation":[{"name":"Center of Excellence in Experimental Solid Mechanics and Dynamics, Fatigue and Fracture Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9840-6225","authenticated-orcid":false,"given":"Majid Reza","family":"Ayatollahi","sequence":"additional","affiliation":[{"name":"Center of Excellence in Experimental Solid Mechanics and Dynamics, Fatigue and Fracture Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3950-6071","authenticated-orcid":false,"given":"Sergio","family":"Cicero","sequence":"additional","affiliation":[{"name":"LADICIM, Departamento de Ciencia e Ingenier\u00eda del Terreno y de los Materiales, Universidad de Cantabria, 39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103815","DOI":"10.1016\/j.euromechsol.2019.103815","article-title":"Antiplane shear stresses in orthotropic plates with lateral blunt notches","volume":"77","author":"Zappalorto","year":"2019","journal-title":"Eur. 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