ANALYTICAL SOLUTIONS OF THE TENSILE STRENGTH AND PREPONDERANT CRACK ANGLE FOR THE I-II MIXED CRACK IN BRITTLE MATERIAL

Abstract

The I-II mixed crack is one of the most common cracks contained in the engineering materials. In this study, the theoretical solutions of the brittle tensile failure capability K_J , the tensile strength σ_c, and the initial fracture angle θ₀ are developed for the engineering materials containing the mode I-II mixed cracks (the crack angle is β) under uniaxial tensile stress loading based on the maximum circumferential stress criterion. Additionally, under the same frame and boundary conditions, it is concluded that the preponderant crack angle β is 68.09 which making the cracks are most easy to fail and propagate; the corresponding brittle tensile capability K_J is 0.97K_IC, and the tensile strength σ_c is σ_c=0.97K_IC/√pa. Based on the results stated above, it is further concluded that, in the engineering structure design, if the tensile strength of materials σ_c is given, the allowed maximum length of cracks a₀ is limited to 0.94K²_IC/pσ_c², which would provide the theoretical foundations for limiting the maximum length of cracks, and detecting cracks in engineering design.

DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1275