An Improved Mathematical Representation of Mohr’s Failure Criterion For Brittle Materials

Abstract

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.