Concept of Equivalent Stress Criterion For Predicting Failure of Brittle Materials

Abstract

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.