An Improved Mathematical Representation of Mohr’s Failure Criterion For Brittle Materials
DOI:
https://doi.org/10.26437/ajar.31.10.2022.17Abstract
Purpose: This paper addresses issues bearing on accuracy neglected by earlier failure theories such as Rankine’s and Mohr’s. The overall aim is thus to present a thorough analysis of Mohr’s failure criterion and offer an improved model.
Design/Methodology/Approach: The foundation of the methodology is Mohr’s criterion for predicting the failure of brittle isotropic homogeneous materials, built on the foundation of test results from three simple cases namely, pure tension, pure compression, and pure torsion. Thus the methodology involves first carrying out a critical analysis of Mohr’s model, followed by encapsulation of Mohr’s three simple monolithic cases in one generic equation of a circle whose parameters can be varied to match specific principal loading conditions more correctly. Experimental data are then used to validate the improved model.
Findings: The work’s output is a material evaluation procedure that consists of a set of simple mathematical tests, any one of which predicting failure first, would then indicate the overall failure of the structural component under investigation. Results show clearly that this approach, i.e. using one parametric generic equation to represent material strength, is not only feasible but also robust. It offers an accurate method for predicting the failure of a brittle material under complex stresses.
Research Limitation: Improvised conditions for biaxial data collection were less than ideal.
Practical implication: The study recommended that other brittle materials beyond cast iron be included in any further studies to broaden the scope of applicability of the findings.
Social implication: The research adds new literature and findings to an old subject. With this new knowledge, bookmakers could shape the way brittle materials are used in engineering design.
Originality / Value: The value of the study lies in the fact that to date very few failure theories exist that cater fully satisfactorily to brittle materials. The rigour of the methodology confers potential for its application beyond brittle materials.
References
Barsanescu, P. D., & Comanici, A. M. (2017). von Mises hypothesis revised. Acta
Mechanica, 228(2), 433-446.
Christensen, R. M. (2018). The ductile/brittle transition provides the critical test for materials
failure theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2210), 20170817.
Christensen, R. M. (2016). Evaluation of ductile/brittle failure theory and derivation of the
ductile/brittle transition temperature. Journal of Applied Mechanics, 83(2), 021001.
Christensen, R., Li, Z., & Gao, H. (2018). An evaluation of the failure modes transition and
the Christensen ductile/brittle failure theory using molecular dynamics. Proceedings of the Royal Society A, 474(2219), 20180361.
Giraldo-Londoño, O., & Paulino, G. H. (2020). A unified approach for topology optimization
with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke. Proceedings of the Royal Society A, 476(2238), 20190861.
Gu, J., & Chen, P. (2018). A failure criterion for homogeneous and isotropic materials
distinguishing the different effects of hydrostatic tension and compression. European Journal of Mechanics-A/Solids, 70, 15-22.
Gu, J., & Chen, P. (2018). A failure criterion for isotropic materials based on Mohr’s failure
plane theory. Mechanics Research Communications, 87, 1-6.
Injeti, S. S., Daraio, C., & Bhattacharya, K. (2019). Metamaterials with engineered failure
load and stiffness. Proceedings of the National Academy of Sciences, 116(48), 23960-23965.
Jeong, S. H., Park, S. H., Choi, D. H., & Yoon, G. H. (2012). Topology optimization
considering static failure theories for ductile and brittle materials. Computers & structures, 110, 116-132.
Lazzarin, P., Campagnolo, A., & Berto, F. (2014). A comparison among some recent energy-
and stress-based criteria for the fracture assessment of sharp V-notched components under Mode I loading. Theoretical and Applied Fracture Mechanics, 71, 21-30.
Pereira, A., Costa, M., Anflor, C., Pardal, J., & Leiderman, R. (2018). Estimating the effective
elastic parameters of nodular cast iron from micro-tomographic imaging and multiscale finite elements: Comparison between numerical and experimental results. Metals, 8(9), 695.
Qu, R.T., Zhang, Z. J., Zhang, P., Liu, Z.Q. & Zhang, Z.F. (2016), Generalized energy failure criterion, Sci Rep, 6 (1) 1-8.
Sun, Y., & Xiang, Z. (2022). A semi-analytical quasi-brittle fracture criterion for elliptical
notches. Engineering Fracture Mechanics, 266, 108405.
Tiraviriyaporn, P., & Aimmanee, S. (2022). Energy-based universal failure criterion and
strength-Poisson's ratio relationship for isotropic materials. International Journal of Mechanical Sciences, 230, 107534.
Vasiliev, V., Lurie, S., & Solyaev, Y. (2021). New approach to failure of pre-cracked brittle
materials based on regularized solutions of strain gradient elasticity. Engineering Fracture Mechanics, 258, 108080.
Wu, S.J., Chin P.C. & Liu H. (2019), Measurement of elastic properties of brittle materials by ultrasonic and indentation methods, Appl Sci, 9 (10) 2067.
Yosibash, Z., & Mittelman, B. (2016). A 3-D failure initiation criterion from a sharp V-notch
edge in elastic brittle structures. European Journal of Mechanics-A/Solids, 60, 70-94.
Yosibash, Z., Mendelovich, V., Gilad, I., & Bussiba, A. (2022). Can the finite fracture
mechanics coupled criterion be applied to V-notch tips of a quasi-brittle steel alloy? Engineering Fracture Mechanics, 269, 108513.
Yu, N. Y., Li, Q., & Chen, Y. H. (2013). Experimental evaluation of the M-integral in an
elastic-plastic material containing multiple defects. Journal of Applied Mechanics, 80(1).
Yu, L., & Wang, T. C. (2019). Generalized Mohr-Coulomb strain criterion for bulk metallic
glasses under complex compressive loading. Scientific Reports, 9(1), 1-9.
Zheng, L., Wang, K., Jiang, Y., Wan, M., & Meng, B. (2022). A new ductile failure criterion for micro/meso scale forming limit prediction of metal foils considering size effect and free surface roughening. International Journal of Plasticity, 157, 103406.
Zuo, S., Hu, C., Zhao, L., Jiao, K., Lei, Z., Huang, D., & Zhu, Z. (2021). Reliability back
analysis of a 3D wedge slope based on the nonlinear Barton-Bandis failure criterion. Engineering Failure Analysis, 128, 105601.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2022 AFRICAN JOURNAL OF APPLIED RESEARCH
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
By submitting and publishing your articles in the African Journal of Applied Research, you agree to transfer the copyright of the Article from the authors to the Journal ( African Journal of Applied Research).
