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.

Purpose: A paucity of proven failure criteria for brittle engineering materials exists, and this paper intends to present and validate a novel concept of equivalent stress criterion for predicting the failure of brittle isotropic homogeneous materials based on the concept of effective causative failure stress. Design/Methodology/Approach: Mathematical modelling is first performed based on strain-state equivalence, followed by conversion to the equivalent causative stress. The model is then validated with experimental and other data and with comparisons to traditional models. The material studied is BS 1452 Grade 250 continuous-cast grey cast iron with a Young’s Modulus of 39 000 MPa and ultimate tensile strength of 290 MPa. The test samples were prepared square in shape 12 mm x 12 mm to enable stresses in two perpendicular directions. Data is generated from uniaxial and bi-axial tests, performed using a standard universal testing machine, INSTRON 880, improvised to enable bi-axial recordings. Findings: Results point consistently to higher fidelity and transparency of the new model in representing the state of stress, especially in the second and fourth quadrants of the principal stress diagram, where Rankine’s criterion completely ignores stress differences and Mohr handles shear stresses in a suboptimal fashion. Both the maximum principal stresses and maximum shear stresses predicted by the proposed model are found to be somewhat greater than those from the traditional models, indicating higher accuracy and greater aggressiveness in prediction. The findings have further revealed that shearing effects play a greater role in the failure of engineering brittle materials than traditional failure theories have considered. Research Limitation: The study involved improvisation to enable biaxial stress recordings. This process was not perfect, resulting in smaller-than-ideal values of the lateral stresses. Practical implication:  The study recommended process and equipment development toward perfecting multiaxial tests. Social implication: The survey will enrich the literature with pertinent design methodology to help in product design, including social-interest products.  Originality / Value: Since truly homogeneous materials are known to withstand very high hydrostatic pressures, direct stresses alone do not constitute valid failure criteria for all loading conditions.