Rational implementation of the Mohr criterion in its general form

Li, Shuguang

Abstract

The Mohr criterion is successfully implemented for brittle materials in its general form based on failure envelopes formulated using quadratic functions. This is probably the first time when the criterion has been made comprehensive enough and yet convenient enough to apply since its publication over 120 years ago. To facilitate the formulation, all stress states at failure are partitioned into two groups and all materials are classified into those of higher and lower brittleness. A failure envelope is constructed rationally for each class of materials without resorting to either an oversimplistic and unreasonable linearisation or an overcomplicated and highly nonlinear formulation. For materials of higher brittleness, the envelope can be defined using a single parabola, whilst for those of lower brittleness, the envelope is defined in a piecewise manner. A new concept of the terminating Mohr's circle (TMC) is introduced which sits at the tensile end as a part of the envelope to terminate the parabola whilst joining the parabolic part of the envelope smoothly. Its diameter varies with the brittleness of the material. It is instrumental both in the partition of stress states and in the classification of materials. The required input data for such formulated Mohr criterion are tensile and compressive strengths only. The procedure of actual applications of the criterion to the assessment of material failure is relatively simple and straightforward as demonstrated in the paper and the schematic is also provided. The failure mode can be predicted in terms of the orientation of failure plane. The formulation is verified for its self-consistency and validated through comparisons with existing criteria and experimental data. The criterion can now be employed in practical failure predictions as a useful means supporting engineering design, especially when brittle materials are concerned.

Citation

Li, S. (2024). Rational implementation of the Mohr criterion in its general form. International Journal of Mechanical Sciences, 279, 109449. https://doi.org/10.1016/j.ijmecsci.2024.109449

• Journal Article Type: Article
• Acceptance Date: Jun 3, 2024
• Online Publication Date: Jun 4, 2024
• Publication Date: Oct 1, 2024
• Deposit Date: Jul 27, 2024
• Publicly Available Date: Jul 31, 2024
• Journal: International Journal of Mechanical Sciences
• Print ISSN: 0020-7403
• Electronic ISSN: 0020-7403
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 279
• Article Number: 109449
• Pages: 109449
• DOI: https://doi.org/10.1016/j.ijmecsci.2024.109449
• Keywords: The Mohr criterion; Brittle material; Failure mode; Failure envelope; Strength; Terminating Mohr's circle (TMC)
• Public URL: https://nottingham-repository.worktribe.com/output/37604371
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0020740324004910?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Rational implementation of the Mohr criterion in its general form; Journal Title: International Journal of Mechanical Sciences; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.ijmecsci.2024.109449; Content Type: article; Copyright: © 2024 The Author(s). Published by Elsevier Ltd.