Sensitivity analysis of notch shape on brittle failure by using uni-bond dual-parameter peridynamics

Abstract

The brittle failure of components weakened by sharp or blunt notches is a topic of active and continuous research. Notches created during the design and manufacturing of structural components give rise to localized stress concentrations, which can generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. To investigate how notches influence the fracture and bearing capacity of brittle materials by using peridynamics (PD), an extended uni-bond dual-parameter peridynamic (UDPD) model that can overcome the fixed Poisson’s ratio in bond-based PD and address the attenuation effect of the nonlocal PD force is developed. The expressions of normal stiffness and tangential stiffness with elastic modulus and Poisson’s ratio are derived and rewritten. Additionally, the critical microstrain energy density for the extended UDPD model is given to judge the fracture initiation, and the validity and accuracy of the proposed model are verified by four examples. Ultimately, six typical types of notches, i.e., rectangular notches, sharp V notches, U notches, blunt V notches, keyhole notches, and VO notches, were selected and investigated in brittle plates with four different tip radii to study the notch sensitivity of brittle failure to notch shape by using the extended UDPD model. The results show that the crack path and bearing capacity of the structure are sensitive to the notch shape and the tip radius of the notch, and a blunt notch with a larger tip radius (U notch, blunt V notch, keyhole notch, and VO notch, tip radius ρ⩾2mm) offers better performance in terms of structural safety than a sharp notch or a notch with a smaller tip radius.