Fracture and Structural Integrity e-ISSN 1971-8993 Open access
Analytical, computational and physical models Vol. 20, No. 77 (2026)

On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion

Author and affiliation details
  • Mujebur Rehaman Department of Mechanical Engineering, PES Institute of Technology & Management, Shivamogga 577204, Visvesvaraya Technological University, Belagavi, India
  • Manjunath Patel Gowdru Chandrashekarappa Corresponding author Department of Mechanical Engineering, Sahyadri College of Engineering & Management, Mangaluru 575007, Visvesvaraya Technological University, Belagavi, India ORCID iD0000-0001-9340-7464 manju09mpm05@gmail.com
  • Mohan T R Department of Mechanical Engineering, Bapuji Institute of Engineering and Technology, Davangere -577004, Visvesvaraya Technological University, Belagavi, India.
  • Shashidhar K Kudari National Institute of Technology Goa, Cuncolium, South Goa District Goa 403 703, India ORCID iD0000-0003-3184-6984
  • Sharanaprabhu C M Department of Mechanical Engineering, PES Institute of Technology & Management, Shivamogga 577204, Visvesvaraya Technological University, Belagavi, India
DOI
10.3221/IGF-ESIS.77.04
Pages
45-55
Published
Licence
CC BY 4.0
Published inVol. 20, No. 77 (2026)Go to the issue

Abstract

In this work, the prediction of crack initiation angle (θo) under mixed mode (I/II) load is estimated from the generalized minimum plastic zone radius (GMPZR) criterion. The paper presents a detailed study on the crack-tip plastic core for asymmetric three-point bend (TPB) specimens of different crack-to-width (a/W) = 0.4-0.7 ratios and loading equivalent angle (βeq) using elastic finite element (FE) analyses. The θo estimated from the FE analysis is compared with the GMPZR criterion, other fracture criteria, and available experimental results. It is found that the θo evaluated from the FE analysis provides the best correlation with the GMPZR criterion among other fracture criteria. The FE results are used to propose an analytical relation between θo and βeq. This proposed relationship can be used to quickly estimate the crack initiation direction/angle for TPB specimens with only βeq available. Finally, the effect of T-stress on θo, will be assessed using as estimated from the GMPZR criterion.

Keywords

Article history

  1. ReceivedUntil the next stage: 77 days
  2. RevisedUntil the next stage: 8 days
  3. AcceptedUntil the next stage: 4 days
  4. Published

How to cite

APA

Rehaman, M., Gowdru Chandrashekarappa, M. P., T R, M., Kudari, S. K., & C M, S. (2026). On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion. Fracture and Structural Integrity, 20(77), 45–55. https://doi.org/10.3221/IGF-ESIS.77.04

IEEE

M. Rehaman, M. P. Gowdru Chandrashekarappa, M. T R, S. K. Kudari, and S. C M, “On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion,” Fracture and Structural Integrity, vol. 20, no. 77, pp. 45–55, 2026, doi: 10.3221/IGF-ESIS.77.04.

MLA

Rehaman, Mujebur, et al. “On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion.” Fracture and Structural Integrity, vol. 20, no. 77, 2026, pp. 45–55. https://doi.org/10.3221/IGF-ESIS.77.04.

Chicago

Rehaman, Mujebur, Manjunath Patel Gowdru Chandrashekarappa, Mohan T R, Shashidhar K Kudari, and Sharnaprabhu C M. 2026. “On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion.” Fracture and Structural Integrity 20 (77): 45–55. https://doi.org/10.3221/IGF-ESIS.77.04.

Harvard

Rehaman, M., Gowdru Chandrashekarappa, M.P., T R, M., Kudari, S.K. and C M, S. (2026) ‘On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion’, Fracture and Structural Integrity, 20(77), pp. 45–55. doi: 10.3221/IGF-ESIS.77.04.

Vancouver

Rehaman M, Gowdru Chandrashekarappa MP, T R M, Kudari SK, C M S. On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion. Fracture and Structural Integrity. 2026;20(77):45-55. doi:10.3221/IGF-ESIS.77.04

BibTeX

@article{rehaman2026, author = {Rehaman, Mujebur and Gowdru Chandrashekarappa, Manjunath Patel and T R, Mohan and Kudari, Shashidhar K and C M, Sharnaprabhu}, title = {On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion}, journal = {Fracture and Structural Integrity}, year = {2026}, volume = {20}, number = {77}, pages = {45--55}, doi = {10.3221/IGF-ESIS.77.04}, url = {https://doi.org/10.3221/IGF-ESIS.77.04}, issn = {1971-8993} }

RIS

TY - JOUR AU - Rehaman, Mujebur AU - Gowdru Chandrashekarappa, Manjunath Patel AU - T R, Mohan AU - Kudari, Shashidhar K AU - C M, Sharnaprabhu TI - On the relationship between crack initiation angle and loading equivalent angle for asymmetric Three-Point Bend Specimens under mixed-mode I/II loading based on GMPZR criterion JO - Fracture and Structural Integrity T2 - Fracture and Structural Integrity PY - 2026 DA - 2026/04/04 VL - 20 IS - 77 SP - 45 EP - 55 DO - 10.3221/IGF-ESIS.77.04 UR - https://doi.org/10.3221/IGF-ESIS.77.04 SN - 1971-8993 ER -

Licence

Creative Commons Attribution 4.0 International

May be shared and adapted, provided appropriate credit is given. Copyright © 2026 Mujebur Rehaman, Manjunath Patel Gowdru Chandrashekarappa, Mohan T R, Shashidhar K Kudari, Sharanaprabhu C M.

Copyright 
Authors are allowed to retain both the copyright and the publishing rights of their articles without restrictions.  

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